Testing composite hypotheses for locally stationary processes

Kenji Sakiyama*, Masanobu Taniguchi

*この研究の対応する著者

研究成果査読

13 被引用数 (Scopus)

抄録

For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.

本文言語English
ページ(範囲)483-504
ページ数22
ジャーナルJournal of Time Series Analysis
24
4
DOI
出版ステータスPublished - 2003 7
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性
  • 応用数学

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