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A two armed optimal response adaptive randomization for ordinal categorical responses with possible misclassification Sequ. Anal. (IF 0.8) Pub Date : 2024-02-06 Soumyadeep Das
A two-treatment optimal target proportion is developed extending the idea of Hu et al. (2006) for phase III clinical trials, where the treatment outcomes are ordinal categorical in nature. Some res...
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Fixed-width confidence interval of log odds ratio in correlated setup for crossover design Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Uttam Bandyopadhyay, Suman Sarkar, Atanu Biswas
This article deals with fixed-width confidence intervals of log odds ratio for correlated setup in crossover design. Related asymptotics are obtained. Procedures are evaluated by simulations, follo...
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Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Evgenii A. Pchelintsev, Serguei M. Pergamenchtchikov, Roman O. Tenzin
In this study, we consider disorder detection problems for statistical models with dependent observations defined by Markov chains in a Bayesian setting for a uniform prior distribution when the nu...
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Data-adaptive symmetric CUSUM for sequential change detection Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Nauman Ahad, Mark A. Davenport, Yao Xie
Detecting change points sequentially in a streaming setting, especially when both the mean and the variance of the signal can change, is often a challenging task. A key difficulty in this context o...
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Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Neeraj Joshi, Sudeep R. Bapat, Raghu Nandan Sengupta
In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (...
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Control charts for high-dimensional time series with estimated in-control parameters Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Rostyslav Bodnar, Taras Bodnar, Wolfgang Schmid
In this article, we study the effect of misspecification caused by fitting the target process in the Phase I analysis of the monitoring procedure on the behavior of several types of multivariate ex...
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A modified Huber loss function for continual reassessment methods in clinical trials Sequ. Anal. (IF 0.8) Pub Date : 2024-01-29 Ling Zhang, Emine Ozgur Bayman, K. D. Zamba
In dose-finding (DF) trials, methods for discovering an optimal criterion that controls toxicity while demonstrating a potential for efficacy have been the subject of statistical research. Although...
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Quickest change detection in statistically periodic processes with unknown post-change distribution Sequ. Anal. (IF 0.8) Pub Date : 2023-12-14 Yousef Oleyaeimotlagh, Taposh Banerjee, Ahmad Taha, Eugene John
Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fix...
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A note on online change point detection Sequ. Anal. (IF 0.8) Pub Date : 2023-12-14 Yi Yu, Oscar Hernan Madrid Padilla, Daren Wang, Alessandro Rinaldo
We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common varian...
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Modeling and quickest detection of a rapidly approaching object Sequ. Anal. (IF 0.8) Pub Date : 2023-12-14 Tim Brucks, Taposh Banerjee, Rahul Mishra
The problem of detecting the presence of a signal that can lead to a disaster is studied. A decision-maker collects data sequentially over time. At some point in time, called the change point, the ...
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Distribution of number of observations required to obtain a cover for the support of a uniform distribution Sequ. Anal. (IF 0.8) Pub Date : 2023-12-14 R. N. Rattihalli
For a given positive number ‘δ′, we consider a sequence of δ− neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U(0,1) distribution, and “stop as soon a...
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Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring Sequ. Anal. (IF 0.8) Pub Date : 2023-09-04 Subhankar Dutta, Farha Sultana, Suchandan Kayal
In this article, we consider the parametric inference, using Type II censored data, based on the tampered random variable (TRV) model for simple step-stress life testing (SSLT). We have taken the m...
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A Sequential Test of Traffic Intensity for the M/M/1 Queueing System Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Murat Sagir
Abstract This paper deals with testing traffic intensity, which is the most important parameter of the M/M/1M/M/1 queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution
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Comparison of Gini indices using sequential approach: Application to the U.S. Small Business Administration data Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Francis Bilson Darku, Dorcas Ofori-Boateng, Bhargab Chattopadhyay
Abstract The comparison of Gini inequality indices is an important study related to regional imbalance in equality. In the design of such a study, both the cost constraints and variability of the difference of inequality indices play an active role. In this article, we compare the Gini inequality indices for two regions under cost constraints leveraging on the concept of sequential analysis. Without
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Two-stage estimation of the combination of location and scale parameter of the exponential distribution under the constraint of bounded risk per unit cost index Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Eisa Mahmoudi, Zahra Nemati, Ashkan Khalifeh
Abstract We consider the problem of bounded risk point estimation for the linear combination of the form θ=eα+dβ,θ=eα+dβ, where αα and ββ are the location and scale parameters of a exponential distribution and e≥0e≥0 and d>0d>0 are constant. We aim to estimate θθ under the modified squared error loss function using the constraint that the risk per unit cost is bounded above with fixed preassigned,
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Detecting an intermittent change of unknown duration Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Grigory Sokolov, Valentin S. Spivak, Alexander G. Tartakovsky
Abstract Oftentimes, in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an overview of existing approaches for intermittent change detection and advocate in favor of a particular setting driven by the intermittent nature of the
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A numerical approach to sequential multi-hypothesis testing for Bernoulli model Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Andrey Novikov
Abstract In this article, we deal with the problem of sequential testing of multiple hypotheses. The main goal is minimizing the expected sample size (ESS) under restrictions on the error probabilities. We take, as a criterion of minimization, a weighted sum of the ESSs evaluated at some points of interest in the parameter space, aiming at its minimization under restrictions on the error probabilities
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An ARL-unbiased modified chart for monitoring autoregressive counts with geometric marginal distributions Sequ. Anal. (IF 0.8) Pub Date : 2023-07-20 Manuel Cabral Morais, Philipp Wittenberg, Sven Knoth
Abstract Geometrically distributed counts arise in the industry. Ideally, they should be monitored using a control chart whose average run length (ARL) function achieves a maximum when the process is in control; that is, the chart is ARL-unbiased. Moreover, its in-control ARL should coincide with a reasonably large and prespecified value. Because dependence among successive geometric counts is occasionally
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Real-time change point detection in linear models using the ranking selection procedure Sequ. Anal. (IF 0.8) Pub Date : 2023-05-23 Chao Gu, Suthakaran Ratnasingam
Abstract We propose a novel sequential change point detection method in linear models. Our method uses a given historical data set to determine the prechange model. Significant features are selected using the ranking procedure, which is an innovative approach aimed at revealing the rank of all features in terms of their effects on the model. We establish the asymptotic properties of the test statistic
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Group-sequential response-adaptive designs for multi-armed trials Sequ. Anal. (IF 0.8) Pub Date : 2023-05-23 Wenyu Liu, D. Stephen Coad
Abstract Several experimental treatments are often compared with a common control in a clinical trial nowadays. A group-sequential design incorporating response-adaptive randomization can help to increase the probability of receiving a more promising treatment for patients in the trial and to detect a treatment effect early so as to benefit the whole population of interest. With such ethical advantages
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Asymptotic optimality theory for active quickest detection with unknown postchange parameters Sequ. Anal. (IF 0.8) Pub Date : 2023-05-23 Qunzhi Xu, Yajun Mei
Abstract The active quickest detection problem with unknown postchange parameters is studied under the sampling control constraint, where there are p local streams in a system but one is only able to take observations from one and only one of these p local streams at each time instant. The objective is to raise a correct alarm as quickly as possible once the change occurs subject to both false alarm
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One-sided maximal inequalities for a randomly stopped Bessel process Sequ. Anal. (IF 0.8) Pub Date : 2023-05-23 Cloud Makasu
Abstract We prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension 1≤α<2. For the special case when α = 1, we obtain a sharp Burkholder-Gundy inequality for Brownian motion as a consequence. An application of the present results is also given.
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Numerical solution of Kiefer-Weiss problems when sampling from continuous exponential families Sequ. Anal. (IF 0.8) Pub Date : 2023-05-23 Andrey Novikov, Andrei Novikov, Fahil Farkhshatov
Abstract In this article, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in Kiefer-Weiss problems. The main goal of the Kiefer-Weiss problem is designing hypothesis tests that minimize the maximum average sample number, over all parameter values, as opposed to both the
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Sequential Detection of an Arbitrary Transient Change Profile by the FMA Test Sequ. Anal. (IF 0.8) Pub Date : 2023-03-21 Fatima Ezzahra Mana, Blaise Kévin Guépié, Igor Nikiforov
Abstract This article addresses the sequential detection of transient changes by using the finite moving average (FMA) test. It is assumed that a change occurs at an unknown (but nonrandom) change point and the duration of postchange period is finite and known. We relax the assumption that the profile of a transient change is chosen so that the log-likelihood ratios of the observations are associated
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Online score statistics for detecting clustered change in network point processes Sequ. Anal. (IF 0.8) Pub Date : 2023-02-16 Rui Zhang, Haoyun Wang, Yao Xie
Abstract We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution that follows a multivariate Hawkes process with exponential decay temporal
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Asymptotic optimality of a robust two-stage procedure in multivariate Bayes sequential estimation Sequ. Anal. (IF 0.8) Pub Date : 2023-01-31 Leng-Cheng Hwang
Abstract Within the Bayesian framework, a robust two-stage procedure is proposed to deal with the problem of multivariate sequential estimation of the unknown mean vector with weighted squared error loss and fixed cost per observation. The proposed procedure depends on the present data but not on the distributions of outcome variables or the prior. It is shown that the proposed procedure shares the
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Exact Inference in a Tetranomial Distribution Sequ. Anal. (IF 0.8) Pub Date : 2023-01-12 Papia Sultana, Manisha Pal, Bikas K. Sinha
Abstract Sequential sampling plans for unbiased estimation of the Bernoulli parameter ‘p’ and its functions have been studied almost 70 years back. An extension of the idea to parametric function estimation in a tetranomial distribution has been considered in this paper. The cell probabilities are taken to be p2, q2, r2 and 2(pq+pr+qr), satisfying p, q, r > 0, p +q +r = 1. Some illustrative examples
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A restricted subset selection procedure for selecting the largest normal mean under heteroscedasticity Sequ. Anal. (IF 0.8) Pub Date : 2023-01-12 Elena M. Buzaianu, Pinyuen Chen, Lifang Hsu
Abstract This article considers the goal of selecting the population with the largest mean among k normal populations when variances are not known. We propose a Stein-type two-sample procedure, denoted by RBCH, for selecting a nonempty random-size subset of size at most m ( 1≤m≤k−1) that contains the population associated with the largest mean, with a guaranteed minimum probability P*, whenever the
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On the exact constants in one-sided maximal inequalities for Bessel processes Sequ. Anal. (IF 0.8) Pub Date : 2023-01-04 Cloud Makasu
Abstract In this paper, we establish a one-sided maximal moment inequality with exact constants for Bessel processes. As a consequence, we obtain an exact constant in the Burkholder-Gundy inequality. The proof of our main result is based on a pure optimal stopping problem of the running maximum process for a Bessel process. The present results extend and complement a number of related results previously
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Designing of Variables Double Sampling Plan Under Rectifying Inspection for Consumer Protection Sequ. Anal. (IF 0.8) Pub Date : 2022-12-21 P. Jeyadurga, S. Balamurali
Abstract Designing of acceptance sampling plans based on operating characteristics fail to prescribe the corrective action for rejected lots although they guarantee the producer’s and the consumer’s protection at their corresponding quality levels. But, rectification sampling inspection plan suggests 100% inspection for rejected lots and hence, the producer’s risk is reduced and also there is a guarantee
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Proof of a Key Inequality for Lattice Event Probabilities with Equal Odds Sequ. Anal. (IF 0.8) Pub Date : 2022-11-25 Bruce Levin, Cheng-Shiun Leu
Abstract Levin and Leu (2021 Levin, B. and Leu, C.-S. (2021). A Key Inequality for Lower Bound Formulas for Lattice Event Probabilities. Sequential Analysis 40(4):554–574. doi:10.1080/07474946.2021.2010417[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) introduced some key inequalities that underlie the lower bound formula for the probability of lattice events when using adaptive members
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Sequential nonparametric estimation of controlled multivariate regression Sequ. Anal. (IF 0.8) Pub Date : 2022-11-25 Sam Efromovich
Abstract The article considers an adaptive sequential nonparametric estimation of a multivariate regression with assigned mean integrated squared error (MISE) and minimax mean stopping time when the estimator matches performance of an oracle knowing all nuisance parameters and functions. It is known that the problem has no solution if regression belongs to a Sobolev class of differentiable functions
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A two-stage design for comparing binomial treatments with a standard Sequ. Anal. (IF 0.8) Pub Date : 2022-11-25 Cecelia K. Schmidt, Elena M. Buzaianu
Abstract We propose a two-stage selection and testing procedure for comparing success rates of several populations among each other and against a desired standard success rate to identify which treatment has the highest rate of success that is also higher than the standard. The design combines elements of both hypothesis testing and statistical selection. As a hybrid two-stage procedure, it allows
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Design and performance evaluation in Kiefer-Weiss problems when sampling from discrete exponential families Sequ. Anal. (IF 0.8) Pub Date : 2022-10-31 Andrey Novikov, Fahil Farkhshatov
Abstract In this article, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in the Kiefer-Weiss problems. For the case of observations following a discrete exponential family, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas
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Sequential change-point detection for skew normal distribution Sequ. Anal. (IF 0.8) Pub Date : 2022-09-13 Peiyao Wang, Wei Ning
Abstract In this article, we propose a modified max-cumulative sum (CUSUM) procedure for detecting changes in parameters of skew normal distribution. The corresponding false alarms frequency and the postchange detection delay are investigated. Asymptotic behaviors of detection delay and theoretical optimality of the detection procedure have been established. Simulations have been conducted to show
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An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis Sequ. Anal. (IF 0.8) Pub Date : 2022-09-13 Srawan Kumar Bishnoi, Nitis Mukhopadhyay
Abstract We develop a new class of purely sequential methodologies under an assumption that the population distribution belongs to a location-scale family. Both asymptotic first-order and second-order theories are put forward with substantial generality under a big and unified tent that successfully lead to a broad set of illustrations. After we identify an appropriately defined optimal strategy under
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Patient-specific dose finding in seamless phase I/II clinical trials Sequ. Anal. (IF 0.8) Pub Date : 2022-09-13 M. Iftakhar Alam, Shantonu Islam Shanto
Abstract This article incorporates a covariate to determine the optimum dose in a seamless phase I/II clinical trial. A binary covariate and its interaction effect are assumed to keep the method simple. Each patient’s outcome is assumed to be trinomial, and the continuation ratio model is utilized to model the dose–response data. The Bayesian approach estimates parameters of the dose–response model
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Bounded risk per unit cost index constraint for sequential estimation of the mean in a two-parameter exponential distribution Sequ. Anal. (IF 0.8) Pub Date : 2022-09-13 Eisa Mahmoudi, Zahra Nemati, Ashkan Khalifeh
Abstract In this article, the two-stage sequential sampling procedure is proposed to estimate the mean of an exponential distribution under the modified square error loss function. The main aim of the article is to consider the associated risk per unit cost function by bounding it from above with a fixed preassigned positive number, ω. We provide the exact distribution of the total sample size, explicit
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Monitoring a Bernoulli process subject to gradual changes in the success rates of a sequence of Bernoulli random variables Sequ. Anal. (IF 0.8) Pub Date : 2022-09-13 Marlo Brown
Abstract We look at a sequence of Bernoulli random variables where the success rates change from θ1 to θ2. We will assume that both the success rates before and after the change are known. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping
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Two-stage and sequential unbiased estimation of N in binomial trials, when the probability of success p is unknown Sequ. Anal. (IF 0.8) Pub Date : 2022-08-29 Yaakov Malinovsky, Shelemyahu Zacks
Abstract We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative binomial experiment having the same p.
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Bayesian sequential joint detection and estimation under multiple hypotheses Sequ. Anal. (IF 0.8) Pub Date : 2022-07-15 Dominik Reinhard, Michael Fauß, Abdelhak M. Zoubir
Abstract We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The optimal method minimizes the expected number of samples while ensuring that the average detection/estimation errors do not exceed a certain level. After
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Sequential common change detection, isolation, and estimation in multiple poisson processes Sequ. Anal. (IF 0.8) Pub Date : 2022-07-15 Yanhong Wu, Wei Biao Wu
Abstract In this article, motivated by detecting the occurrence of an epidemic when the arrival rates of patients increase in a portion of M panels or detecting the deterioration of a system composed of M independent components that causes an increase in failure rates in a portion of components, we consider the detection of a common change when M independent Poisson processes are monitored simultaneously
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A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population Sequ. Anal. (IF 0.8) Pub Date : 2022-07-15 Andrey Novikov, Andrei Novikov, Fahil Farkhshatov
Abstract We present a computational approach to the solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with
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Optimal group sequential tests with groups of random size Sequ. Anal. (IF 0.8) Pub Date : 2022-07-15 A. Novikov, X. I. Popoca-Jiménez
Abstract We consider sequential hypothesis testing based on observations that are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent and their distributions are known and that the groups are formed independent of the observations. We are concerned with a problem of testing a simple hypothesis
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A new formulation of minimum risk fixed-width confidence interval (MRFWCI) estimation problems for a normal mean with illustrations and simulations: Applications to air quality data Sequ. Anal. (IF 0.8) Pub Date : 2022-07-15 Nitis Mukhopadhyay, Swathi Venkatesan
Abstract Research on classical fixed-width confidence interval (FWCI) estimation problems for a normal mean when the variance remains unknown have steadily moved along under a zero-one loss function. On the other hand, minimum risk point estimation (MRPE) problems have grown largely under a squared error loss function plus sampling cost. However, the FWCI problems customarily do not take into account
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A sequential decoding procedure for pooled quantitative measure Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Yunning Zhong, Ping Xu, Siming Zhong, Juan Ding
Abstract Group testing (pooling) is a commonly used method while screening for rare diseases, especially for large-scale screening. In recent years there has been growing interest in direct analysis of quantitative measures to take advantage of full information. In this study, we develop a pooling procedure for identification of infected specimens and the measurement is quantitative. Exclusive simulations
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Asymptotically optimal robust information-based quick detection for general stochastic models with nonparametric postchange uncertainty Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Valérie Girardin, Victor Konev, Serguei Pergamenchtchikov
Abstract By making use of Kullback-Leibler information, we develop a new approach for the quickest detection problem for general statistical models with dependent observations and unknown postchange distributions; the postchange distribution depends on either unknown informative parameters or unknown nonparametric infinite-dimensional nuisance functions. For such models, we introduce a robust risk
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Robust change detection for large-scale data streams Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Ruizhi Zhang, Yajun Mei, Jianjun Shi
Abstract Robust change point detection for large-scale data streams has many real-world applications in industrial quality control, signal detection, and biosurveillance. Unfortunately, it is highly nontrivial to develop efficient schemes due to three challenges: (1) the unknown sparse subset of affected data streams, (2) the unexpected outliers, and (3) computational scalability for real-time monitoring
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Economical design of multiple deferred (dependent) state repetitive group sampling plan based on truncated life test under exponentiated half-logistic distribution Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 G. Kannan, P. Jeyadurga, S. Balamurali
Abstract The design of a multiple deferred (dependent) state repetitive group sampling plan for exponentiated half-logistic distributed percentile life assurance under time-truncated life test is considered in this article. In this research, tables are provided to choose the design parameters of the proposed plan determined for different percentile ratios using the method of two points on the operating
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General optimal stopping with linear cost Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Sören Christensen, Tobias Sohr
Abstract This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs as they naturally arise in many problems in sequential decision making. Using an auxiliary function of maximum representation type, conditions are given to guarantee the optimal stopping time to be of threshold type. The optimal threshold is then
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SPRT-based cooperative spectrum sensing with performance requirements in cognitive unmanned aerial vehicle networks (CUAVNs) Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Jun Wu, Pei Li, Jia Zhang, Zehao Chen, Jianrong Bao
Abstract In view of the spectrum scarcity of unmanned aerial vehicles’ (UAVs) communication systems, cooperative spectrum sensing (CSS) is used to identify the available spectrum for cognitive UAV networks (CUAVNs). Due to the flexible locations of flying UAVs, we first design an intraframe cooperation way to replace the traditional interframe cooperation to achieve CSS in this article. Considering
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Adversarially robust sequential hypothesis testing Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Shuchen Cao, Ruizhi Zhang, Shaofeng Zou
Abstract The problem of sequential hypothesis testing is studied, where samples are taken sequentially, and the goal is to distinguish between the null hypothesis where the samples are generated according to a distribution p and the alternative hypothesis where the samples are generated according to a distribution q. The defender (decision maker) aims to distinguish the two hypotheses using as few
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Three-stage minimum risk point estimation with termination defined via Gini’s mean difference Sequ. Anal. (IF 0.8) Pub Date : 2022-05-17 Jun Hu, Dinh Dong Pham
Abstract In this article, we revisit the classic inference problem of minimum risk point estimation for an unknown normal mean when the variance also remains unknown. We propose an alternative three-stage sampling procedure with termination defined via Gini’s mean difference rather than the traditional sample standard deviation. A number of asymptotic properties are investigated both theoretically
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An algorithm for probabilistic solution of parabolic PDEs Sequ. Anal. (IF 0.8) Pub Date : 2021-12-29 M. Haneche, K. Djaballah, K. Khaldi
Abstract The aim of this work is to approximate the trajectory solution of parabolic partial differential equations (PDEs) by the probabilistic method. This method is based on the representation of Feynman-Kac and Monte Carlo methods. As an alternative to classical Monte Carlo, here we employ quasi–Monte Carlo methods and propose some solutions to the problem of using this alternative through a more
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Two-stage procedure in a first-order autoregressive process and comparison with a purely sequential procedure Sequ. Anal. (IF 0.8) Pub Date : 2022-01-06 Soudabe Sajjadipanah, Eisa Mahmoudi, Mohammadsadegh Zamani
Abstract A two-stage procedure in a first-order autoregressive model (AR(1)) is considered that investigates the point and the interval estimation of parameters based on the least squares estimator. The two-stage procedure is shown to be as effective as the best fixed-sample-size procedure. In this regard, the significant properties of the procedure, such as asymptotic risk efficiency, asymptotic efficiency
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On a class of purely sequential procedures with applications to estimation and ranking and selection problems Sequ. Anal. (IF 0.8) Pub Date : 2021-12-27 Neeraj Joshi, Sudeep R. Bapat
Abstract In this article, we develop a general class of purely sequential procedures and obtain the associated first- and second-order asymptotics for the expected sample size and regret. We establish that many estimation and ranking and selection problems can be handled with the help of the proposed class of sequential procedures. A brief simulation analysis is carried out in support of the accuracy
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Binomial early stopping times Sequ. Anal. (IF 0.8) Pub Date : 2021-12-27 Nick Mulgan
Abstract Sequential analysis for the purposes of possibly stopping a trial early is important whenever a result must be obtained as quickly as possible for public health, economic, or other reasons. A dominant research stream since the middle of the 20th century has been the challenge of generalizing Wald’s sequential probability ratio test (SPRT) to include composite alternative hypotheses. This article
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Analytical calculations of various powers assuming normality Sequ. Anal. (IF 0.8) Pub Date : 2021-12-23 Ying-Ying Zhang, Teng-Zhong Rong, Man-Man Li
Abstract Assuming normality for the prior and the likelihood, we calculate the rejection region, the power or the conditional power, and the predictive power or the conditional predictive power of one-sided hypotheses with a nonzero threshold that corresponds to a noninferiority test for two-arm trials for five different scenarios, which are nonsequential trials with classical power and Bayesian power
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On sequential confidence interval in a stationary Gaussian process Sequ. Anal. (IF 0.8) Pub Date : 2021-12-27 Pritam Sarkar, Uttam Bandyopadhyay
Abstract In this article we concentrate on fixed accuracy intervals of the common variance when the data arise from a Gaussian process with order 1 autoregressive covariance structure. Our approach includes the maximum likelihood method and least squares method for estimating the parameters in this process. We provide necessary asymptotic results and carry out numerical evaluations.
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A key inequality for lower bound formulas for lattice event probabilities Sequ. Anal. (IF 0.8) Pub Date : 2022-01-04 Bruce Levin, Cheng-Shiun Leu
Abstract We introduce and discuss some key inequalities that underlie the lower bound formula for the probability of lattice events in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. The present work combines the notion of lattice events—as previously discussed for the nonadaptive member of the family—with the positive cumulative sum property for the adaptive