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

Junichi Hirukawa, Masanobu Taniguchi

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)640-688
Number of pages49
JournalJournal of Statistical Planning and Inference
Volume136
Issue number3
DOIs
Publication statusPublished - 2006 Mar 1

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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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