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Validation Data-Located Modification for the Multilevel Analysis of Miscategorized Nominal Response with Covariates Subject to Measurement Error Math. Meth. Stat. Pub Date : 2023-12-23 Maryam Ahangari, Mousa Golalizadeh, Zahra Rezaei Ghahroodi
Abstract In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might
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Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality Math. Meth. Stat. Pub Date : 2023-12-23 Narayanaswamy Balakrishnan, Jan Rychtář, Dewey Taylor
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Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates Math. Meth. Stat. Pub Date : 2023-12-23 Kouakou Mathias Amani, Ouagnina Hili, Konan Jean Geoffroy Kouakou
Abstract The marginalized zero-inflated poisson (MZIP) regression model quantifies the effects of an explanatory variable in the mixture population. Also, in practice the variables are usually partially observed. Thus, we first propose to study the maximum likelihood estimator when all variables are observed. Then, assuming that the probability of selection is modeled using mixed covariates (continuous
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Information Generating Function of $$\boldsymbol{k}$$ -Record Values and Its Applications Math. Meth. Stat. Pub Date : 2023-09-19 Manoj Chacko, Annie Grace
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Sharp Lower Bound for Regression with Measurement Errors and Its Implication for Ill-Posedness of Functional Regression Math. Meth. Stat. Pub Date : 2023-09-19 Sam Efromovich
Abstract Nonparametric regression estimation with Gaussian measurement errors in predictors is a classical statistical problem. It is well known that the errors dramatically slow down the rate of regression estimation, and this paper complement that result by presenting a sharp constant. Then an interesting example of using this sharp constant to discover a new curse of dimensionality in functional
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Numerical Solution of Stochastic Mixed Volterra–Fredholm Integral Equations Driven by Space-Time Brownian Motion via Two-Dimensional Triangular Functions Math. Meth. Stat. Pub Date : 2023-09-19 F. Hosseini Shekarabi, M. Khodabin
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Multivariate Doubly Truncated Moments for a Class of Multivariate Location-Scale Mixture of Elliptical Distributions Math. Meth. Stat. Pub Date : 2023-09-19 Xiangyu Han, Chuancun Yin
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Improved Estimators of Tail Index and Extreme Quantiles under Dependence Serials Math. Meth. Stat. Pub Date : 2023-08-07 Mamadou Aliou Barry, El Hadji Deme, Aba Diop, Solym M. Manou-Abi
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A Discrete Analogue of Terrell’s Characterization of Rectangular Distributions Math. Meth. Stat. Pub Date : 2023-08-07 Nickos Papadatos
Abstract Terrell [18] showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular (uniform over some interval) distributions. In the present note it is proved that the same is true for the discrete case, in the sense that the correlation coefficient attains its maximal value only for discrete
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Distributions Derived from the Continuous Iteration of the Hyperbolic Sine Function Math. Meth. Stat. Pub Date : 2023-08-07 Yann Dijoux
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Quantile Based Geometric Vitality Function of Order Statistics Math. Meth. Stat. Pub Date : 2023-04-26 E. I. Abdul Sathar, Veena L. Vijayan
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Reliability Bounds of Dependent Circular Consecutive $$\boldsymbol{k}$$ -out-of- $$\boldsymbol{n:G}$$ Systems Math. Meth. Stat. Pub Date : 2023-04-26 Megraoui Fatima Zohra, Belaloui Soheir
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Rates of the Strong Uniform Consistency for the Kernel-Type Regression Function Estimators with General Kernels on Manifolds Math. Meth. Stat. Pub Date : 2023-04-26 Salim Bouzebda, Nourelhouda Taachouche
Abstract In the present paper, we develop strong uniform consistency results for the generic kernel (including the kernel density estimator) on Riemannian manifolds with Riemann integrable kernels in order to accomplish these difficult tasks. The kernels of the Vapnik-Chervonenkis class that are commonly utilized in statistical problems are different to the isotropic kernels we address in this paper
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Gaussian Approximation for Penalized Wasserstein Barycenters Math. Meth. Stat. Pub Date : 2023-04-26 Nazar Buzun
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Tail and Quantile Estimation for Real-Valued $$\boldsymbol{\beta}$$ -Mixing Spatial Data Math. Meth. Stat. Pub Date : 2023-03-03 Tchamiè Tchazino, Sophie Dabo-Niang, Aliou Diop
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What Intraclass Covariance Structures Can Symmetric Bernoulli Random Variables Have? Math. Meth. Stat. Pub Date : 2023-03-03 Iosif Pinelis
Abstract The covariance matrix of random variables \(X_{1},\dots,X_{n}\) is said to have an intraclass covariance structure if the variances of all the \(X_{i}\)’s are the same and all the pairwise covariances of the \(X_{i}\)’s are the same. We provide a possibly surprising characterization of such covariance matrices in the case when the \(X_{i}\)’s are symmetric Bernoulli random variables.
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Tail Maximal Dependence in Bivariate Models: Estimation and Applications Math. Meth. Stat. Pub Date : 2023-03-03 Ning Sun, Chen Yang, Ričardas Zitikis
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Information Generating Function of Record Values Math. Meth. Stat. Pub Date : 2022-11-07 Zohreh Zamani, Omid Kharazmi, Narayanaswamy Balakrishnan
Abstract In the present work, we study the information generating (IG) function of record values and examine some main properties of it. We establish some comparison results associated with the IG measure of record values. We show that under equality of two given IG measures of upper record values, the corresponding parent distributions can be determined uniquely. We also present some bounds for the
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Robbins–Monro Algorithm with $$\boldsymbol{\psi}$$ -Mixing Random Errors Math. Meth. Stat. Pub Date : 2022-11-07 AbdelKader El Moumen, Salim Benslimane, Samir Rahmani
Abstract In this work, we first establish exponential inequalities for the Robbins–Monro’s algorithm under \(\psi\)-mixing random errors. Then, we present a numerical application that uses the main result of this work to approximate the theoretical solution of the objective function.
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Statistical Inference in a Zero-Inflated Bell Regression Model Math. Meth. Stat. Pub Date : 2022-11-07 Essoham Ali, Mamadou Lamine Diop, Aliou Diop
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Varentropy of Past Lifetimes Math. Meth. Stat. Pub Date : 2022-09-28 Francesco Buono, Maria Longobardi, Franco Pellerey
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Bounds on the Expectations of $$\boldsymbol{L}$$ -Statistics Based on iid Life Distributions Math. Meth. Stat. Pub Date : 2022-09-28 Tomasz Rychlik
Abstract We consider the order statistics based on independent identically distributed non-negative random variables. We determine sharp upper bounds on the expectations of arbitrary linear combinations of order statistics, expressed in the scale units being the \(p\)th roots of \(p\)th raw moments of original variables for various \(p\geq 1\). The bounds are more precisely described for the single
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Jensen’s Inequality Connected with a Double Random Good Math. Meth. Stat. Pub Date : 2022-09-28 Pierpaolo Angelini, Fabrizio Maturo
Abstract In this paper, we define a multiple random good of order \(2\) denoted by \(X_{12}\) whose possible values are of a monetary nature. A two-risky asset portfolio is a multiple random good of order \(2\). It is firstly possible to establish its expected return by using a linear and quadratic metric. We secondly establish the expected return on \(X_{12}\) denoted by \(\mathbf{P}(X_{12})\) by
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D-Optimal Designs for the Mitscherlich Non-Linear Regression Function Math. Meth. Stat. Pub Date : 2022-07-18 Maliheh Heidari, Md Abu Manju, Pieta C. IJzerman-Boon, Edwin R. van den Heuvel
Abstract Mitscherlich’s function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. It has many applications, in particular in the field of measurement reliability. Optimal designs for estimation of this function have been constructed only for normally distributed responses with homoscedastic variances. In
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Matrix Variate Distribution Theory under Elliptical Models—V: The Non-Central Wishart and Inverted Wishart Distributions Math. Meth. Stat. Pub Date : 2022-07-18 Francisco J. Caro-Lopera, Graciela González Farías, N. Balakrishnan
Abstract The non-central Wishart and inverted Wishart distributions are studied in this work under elliptical models; some distributional results are based on some generalizations of the well-known Kummer relations, which leds us to determine that some moments have a polynomial representation. Then the non-central \(F\) and ‘‘studentized Wishart’’ distributions are derived in a general setting. After
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Local Dvoretzky–Kiefer–Wolfowitz Confidence Bands Math. Meth. Stat. Pub Date : 2022-05-30 Odalric-Ambrym Maillard
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Inferential Results for a New Inequality Curve Math. Meth. Stat. Pub Date : 2022-05-30 Youri Davydov, Francesca Greselin
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A Necessary Bayesian Nonparametric Test for Assessing Multivariate Normality Math. Meth. Stat. Pub Date : 2022-05-30 Luai Al-Labadi, Forough Fazeli Asl, Zahra Saberi
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Bounds on the Expectations of $$\boldsymbol{L}$$ -statistics from Iid Symmetric Populations in Various Scale Units Math. Meth. Stat. Pub Date : 2022-05-30 Tomasz Rychlik
Abstract We consider the order statistics \(X_{1:n},\ldots,X_{n:n}\) based on independent identically symmetrically distributed random variables. We determine sharp upper bounds in the properly centered linear combinations of order statistics \(\sum_{i=1}^{n}c_{i}(X_{i:n}-\mu)\), where \((c_{1},\ldots,c_{n})\) is an arbitrary vector of coefficients from the \(n\)-dimensional real space, and \(\mu\)
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Censored Gamma Regression with Uncertain Censoring Status Math. Meth. Stat. Pub Date : 2022-03-29 Jean-François Dupuy
Abstract In this paper, we consider the problem of censored Gamma regression when the censoring status is missing at random. Three estimation methods are investigated. They consist in solving a censored maximum likelihood estimating equation where missing data are replaced by values adjusted using either regression calibration or multiple imputation or inverse probability weights. We show that the
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Selecting an Augmented Random Effects Model Math. Meth. Stat. Pub Date : 2022-03-29 A. L. Rukhin
Abstract There are many collaborative studies where the data are discrepant while uncertainty estimates reported in each study cannot be relied upon. The classical commonly used random effects model explains this phenomenon by additional noise with a constant heterogeneity variance. This assumption may be inadequate especially when the smallest uncertainty values correspond to the cases which are most
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Applying the Solution for the First Multiplicity of Types Equation to Calculate Exact Approximations of the Probability Distributions of Statistical Values Math. Meth. Stat. Pub Date : 2022-03-29 A. K. Melnikov
Abstract We consider here the use of the solution for the first multiplicity of types equation to compute exact probability distributions of statistical values and their exact approximations. We consider \({\Delta}\)-exact distributions as their exact approximations; \({\Delta}\)-exact distributions differ from exact distributions by no more than a predetermined, arbitrarily small value \({\Delta}\)
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On Some Models of Ordered Random Variables and Characterizations of Distributions Math. Meth. Stat. Pub Date : 2022-03-25 Mahdi Tavangar, Ismihan Bayramoglu
Abstract The concept of extended neighboring order statistics introduced in Asadi et al. (2001) is a general model containing models of ordered random variables that are included in the generalized order statistics. This model also includes several models of ordered random variables that are not included in the generalized order statistics and is a helpful tool in unifying characterization results
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On a Time Dependent Divergence Measure between Two Residual Lifetime Distributions Math. Meth. Stat. Pub Date : 2022-03-25 Zahra Mansourvar, Majid Asadi
Abstract Recently, a time-dependent measure of divergence has been introduced by Mansourvar and Asadi (2020) to assess the discrepancy between the survival functions of two residual lifetime random variables. In this paper, we derive various time-dependent results on the proposed divergence measure in connection to other well-known measures in reliability engineering. The proposed criterion is also
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Optimal Rates for Nonparametric F-Score Binary Classification via Post-Processing Math. Meth. Stat. Pub Date : 2021-09-07 Evgenii Chzhen
Abstract This work studies the problem of binary classification with the F-score as the performance measure. We propose a post-processing algorithm for this problem which fits a threshold for any score base classifier to yield high F-score. The post-processing step involves only unlabeled data and can be performed in logarithmic time. We derive a general finite sample post-processing bound for the
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Adaptive Minimax Testing for Circular Convolution Math. Meth. Stat. Pub Date : 2021-09-07 Sandra Schluttenhofer, Jan Johannes
Abstract Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing procedures using a projection approach. The structure of the optimal tests depends on regularity and ill-posedness parameters of the model, which are unknown
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Bounding the Expectation of the Supremum of Empirical Processes Indexed by Hölder Classes Math. Meth. Stat. Pub Date : 2021-08-31 Schreuder, N.
Abstract In this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by Hölder classes of any smoothness and for any distribution supported on a bounded set in \(\mathbb{R}^{d}\). These results can alternatively be seen as non-asymptotic risk bounds, when the unknown distribution is estimated by its empirical counterpart, based on \(n\) independent observations
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Optimal Adaptive Estimation on $${\mathbb{R}}$$ or $${\mathbb{R}}^{{+}}$$ of the Derivatives of a Density Math. Meth. Stat. Pub Date : 2021-08-31 F. Comte, C. Duval, O. Sacko
Abstract In this paper, we consider the problem of estimating the \(d\)-th order derivative \(f^{(d)}\) of a density \(f\), relying on a sample of \(n\) i.i.d. observations \(X_{1},\dots,X_{n}\) with density \(f\) supported on \({\mathbb{R}}\) or \({\mathbb{R}}^{+}\). We propose projection estimators defined in the orthonormal Hermite or Laguerre bases and study their integrated \({\mathbb{L}}^{2}\)-risk
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Multi-level Bayes and MAP Monotonicity Testing Math. Meth. Stat. Pub Date : 2021-08-31 Yu. Golubev, C. Pouet
Abstract In this paper, we develop Bayes and maximum a posteriori probability (MAP) approaches to monotonicity testing. In order to simplify this problem, we consider a simple white Gaussian noise model and with the help of the Haar transform we reduce it to the equivalent problem of testing positivity of the Haar coefficients. This approach permits, in particular, to understand links between monotonicity
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Kernel Selection in Nonparametric Regression Math. Meth. Stat. Pub Date : 2021-08-31 H. Halconruy, N. Marie
Abstract In the regression model \(Y=b(X)+\sigma(X)\varepsilon\), where \(X\) has a density \(f\), this paper deals with an oracle inequality for an estimator of \(bf\), involving a kernel in the sense of Lerasle et al. [13], selected via the PCO method. In addition to the bandwidth selection for kernel-based estimators already studied in Lacour et al. [12] and Comte and Marie [3], the dimension selection
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State Occupation Probabilities in Non-Markov Models Math. Meth. Stat. Pub Date : 2020-01-24 M. Overgaard
The consistency of the Aalen—Johansen-derived estimator of state occupation probabilities in non-Markov multi-state settings is studied and established via a new route. This new route is based on interval functions and relies on a close connection between additive and multiplicative transforms of interval functions, which is established. Under certain assumptions, the consistency follows from explicit
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Admissibility of Invariant Tests for Means with Covariates Math. Meth. Stat. Pub Date : 2020-01-24 Ming-Tien Tsai
For a multinormal distribution with a p-dimensional mean vector θ and an arbitrary unknown dispersion matrix Σ, Rao ([8], [9]) proposed two tests for the problem of testing H0: θ1 = 0, θ2 = 0, Σ unspecified, versus H1: θ1 ≠ 0, θ2 = 0, Σ unspecified. These tests are known as Rao’s W-test and Rao’s U-test, respectively. In this paper, it is shown that Rao’s U-test is admissible while Hotelling’s T2-test
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Relative Error Prediction for Twice Censored Data Math. Meth. Stat. Pub Date : 2020-01-24 S. Khardani
In this paper we consider the problem of non-parametric relative regression for twice censored data. We introduce and study a new estimate of the regression function when it is appropriate to assess performance in terms of mean squared relative error of prediction. We establish the uniform consistency with rate over a compact set and asymptotic normality of the estimator suitably normalized. The asymptotic
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An Asymptotically Optimal Transform of Pearson’s Correlation Statistic Math. Meth. Stat. Pub Date : 2020-01-24 I. Pinelis
It is shown that for any correlation-parametrized model of dependence and any given significance level α ∈ (0, 1), there is an asymptotically optimal transform of Pearson’s correlation statistic R, for which the generally leading error term for the normal approximation vanishes for all values ρ ∈ (−1, 1) of the correlation coefficient. This general result is then applied to the bivariate normal (BVN)
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On the Skewness Order of van Zwet and Oja Math. Meth. Stat. Pub Date : 2020-01-24 A. Eberl, B. Klar
Van Zwet (1964) [16] introduced the convex transformation order between two distribution functions F and G, defined by F ≤cG if G−1 ∘ F is convex. A distribution which precedes G in this order should be seen as less right-skewed than G. Consequently, if F ≤cG, any reasonable measure of skewness should be smaller for F than for G. This property is the key property when defining any skewness measure
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Maxiset Point of View for Signal Detection in Inverse Problems Math. Meth. Stat. Pub Date : 2019-09-27 F. Autin, M. Clausel, J.-M. Freyermuth, C. Marteau
This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robust version of these maxisets allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct
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Central Limit Theorems for Conditional Empirical and Conditional U -Processes of Stationary Mixing Sequences Math. Meth. Stat. Pub Date : 2019-09-27 S. Bouzebda, B. Nemouchi
In this paper we are concerned with the weak convergence to Gaussian processes of conditional empirical processes and conditional U-processes from stationary β-mixing sequences indexed by classes of functions satisfying some entropy conditions. We obtain uniform central limit theorems for conditional empirical processes and conditional U-processes when the classes of functions are uniformly bounded
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Density Deconvolution with Small Berkson Errors Math. Meth. Stat. Pub Date : 2019-09-27 R. Rimal, M. Pensky
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some cases, the unknown density estimator can be obtained by simple averaging without using kernels. However, this may not be the case when Berkson errors are asymptotically
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The Empirical Process of Residuals from an Inverse Regression Math. Meth. Stat. Pub Date : 2019-08-05 T. Kutta, N. Bissantz, J. Chown, H. Dette
In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated using a series estimator motivated by a spectral cutoff technique. Further, we investigate the empirical process of residuals from this regression, and show that it
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On Predictive Density Estimation under α-Divergence Loss Math. Meth. Stat. Pub Date : 2019-08-05 A. L’Moudden, È. Marchand
Based on X ∼ Nd(θ, σ 2 X Id), we study the efficiency of predictive densities under α-divergence loss Lα for estimating the density of Y ∼ Nd(θ, σ 2 Y Id). We identify a large number of cases where improvement on a plug-in density are obtainable by expanding the variance, thus extending earlier findings applicable to Kullback-Leibler loss. The results and proofs are unified with respect to the dimension
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Asymptotic Theory for Longitudinal Data with Missing Responses Adjusted by Inverse Probability Weights Math. Meth. Stat. Pub Date : 2019-08-05 R. M. Balan, D. Jankovic
In this article, we propose a new method for analyzing longitudinal data which contain responses that are missing at random. This method consists in solving the generalized estimating equation (GEE) of [8] in which the incomplete responses are replaced by values adjusted using the inverse probability weights proposed in [17]. We show that the root estimator is consistent and asymptotically normal,
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A Multiple Hypothesis Testing Approach to Detection Changes in Distribution Math. Meth. Stat. Pub Date : 2019-08-05 G. Golubev, M. Safarian
Let X1, X2,... be independent random variables observed sequentially and such that X1,..., Xθ−1 have a common probability density p0, while Xθ, Xθ+1,... are all distributed according to p1 ≠ p0. It is assumed that p0 and p1 are known, but the time change θ ∈ ℤ+ is unknown and the goal is to construct a stopping time τ that detects the change-point θ as soon as possible. The standard approaches to this
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On the Asymptotic Power of Tests of Fit under Local Alternatives in Autoregression Math. Meth. Stat. Pub Date : 2019-08-05 M. V. Boldin
We consider a stationary AR(p) model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and the tests of Kolmogorov’s and ω2 type are constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of these tests under
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A Semi-Parametric Mode Regression with Censored Data Math. Meth. Stat. Pub Date : 2019-05-03 S. Khardani
In this work we suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + ϵ, where m(·) belongs to some parametric class {\({m_\beta}(\cdot):\beta \in \mathbb{K}\)} and the error ϵ is independent of the covariate X. The response Y is subject to random right censoring. Using a nonlinear mode regression, a new estimation procedure for the true unknown parameter vector β0is proposed
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Density Estimation for RWRE Math. Meth. Stat. Pub Date : 2019-05-03 A. Havet, M. Lerasle, É. Moulines
We consider the problem of nonparametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We build several density estimators using the beta-moments of this distribution. Then we apply the Goldenschluger-Lepski method to select an estimator satisfying an oracle type inequality. We obtain non-asymptotic bounds for the supremum
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A Large Deviation Approximation for Multivariate Density Functions Math. Meth. Stat. Pub Date : 2019-05-03 C. Joutard
We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model
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Bayesian Predictive Distribution for a Negative Binomial Model Math. Meth. Stat. Pub Date : 2019-05-03 Y. Hamura, T. Kubokawa
Estimation of the predictive probability function of a negative binomial distribution is addressed under the Kullback—Leibler risk. An identity that relates Bayesian predictive probability estimation to Bayesian point estimation is derived. Such identities are known in the cases of normal and Poisson distributions, and the paper extends the result to the negative binomial case. By using the derived
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Outliers and the Ostensibly Heavy Tails Math. Meth. Stat. Pub Date : 2019-05-03 L. Klebanov, I. Volchenkova
The aim of the paper is to show that the presence of one possible type of outliers is not connected to that of heavy tails of the distribution. In contrary, typical situation for outliers appearance is the case of compactly supported distributions.
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On the Power of Pearson’s Test under Local Alternatives in Autoregression with Outliers Math. Meth. Stat. Pub Date : 2019-05-03 M. V. Boldin
We consider a stationary linear AR(p) model with contamination (gross errors in the observations). The autoregression parameters are unknown, as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of the empirical distribution function is defined and a test of Pearson’s chi-square type is constructed for testing hypotheses on the distribution of innovations
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Asymptotic Distribution of Least Squares Estimators for Linear Models with Dependent Errors: Regular Designs Math. Meth. Stat. Pub Date : 2019-02-05 E. Caron, S. Dede
We consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result of Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and the error process.We show that for a large class of designs, the asymptotic covariance matrix is as simple as in the independent and identically