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

    Fingerprint

    Locally Stationary Processes
    Local area networks
    Statistics
    Theorem
    Contiguous Alternatives
    Adaptive Estimation
    Optimal Estimation
    Asymptotically Optimal
    Unknown Parameters
    Asymptotic distribution
    Innovation
    Robustness
    Unknown
    Testing
    Stationary process
    Class

    Keywords

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

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Applied Mathematics
    • Statistics and Probability

    Cite this

    LAN theorem for non-Gaussian locally stationary processes and its applications. / Hirukawa, Junichi; Taniguchi, Masanobu.

    In: Journal of Statistical Planning and Inference, Vol. 136, No. 3, 01.03.2006, p. 640-688.

    Research output: Contribution to journalArticle

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