Abstract

The paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of the unknown parameters we consider the tapered Whittle estimator and the simplified tapered Whittle estimators. We show that under broad regularity conditions on the spectral density of the model these estimators are asymptotically statistically equivalent, in the sense that these estimators possess the same asymptotic properties. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory.

中文翻译：

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具有锥形数据的稳态线性模型谱参数的简化 Whittle 估计器

摘要

本文关注的是使用锥形数据对平稳模型的谱参数进行统计估计。作为未知参数的估计器，我们考虑锥形 Whittle 估计器和简化的锥形 Whittle 估计器。我们证明，在模型谱密度的广泛规律性条件下，这些估计量在统计上是渐近等效的，因为这些估计量具有相同的渐近性质。所考虑的过程将是具有记忆的离散时间和连续时间高斯、线性或 Lévy 驱动的线性过程。