LAN theorem for non-Gaussian locally stationary processes and its applications

Junichi Hirukawa; Masanobu Taniguchi

doi:10.1016/j.jspi.2004.08.017

LAN theorem for non-Gaussian locally stationary processes and its applications

Junichi Hirukawa, Masanobu Taniguchi

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.

Original language	English
Pages (from-to)	640-688
Number of pages	49
Journal	Journal of Statistical Planning and Inference
Volume	136
Issue number	3
DOIs	https://doi.org/10.1016/j.jspi.2004.08.017
Publication status	Published - 2006 Mar 1

Keywords

Adaptive estimation
Asymptotically efficient estimator
Local asymptotic normality
Locally stationary process
Non-Gaussian robustness
Optimal test

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.",

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AB - For a class of locally stationary processes introduced by Dahlhaus, we derive the LAN theorem under non-Gaussianity and apply the results to asymptotically optimal estimation and testing problems. For a class F of statistics which includes important statistics, we derive the asymptotic distributions of statistics in F under contiguous alternatives of unknown parameter. Because the asymptotics depend on the non-Gaussianity of the process, we discuss the non-Gaussian robustness. An interesting feature of effect of non-Gaussianity is elucidated in terms of LAN. Furthermore, the LAN theorem is applied to adaptive estimation when the innovation density is unknown.

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KW - Locally stationary process

KW - Non-Gaussian robustness

KW - Optimal test

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