Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes

Masanobu Taniguchi*

*この研究の対応する著者

研究成果: Article査読

15 被引用数 (Scopus)

抄録

Let {Xt} be a Gaussian ARMA process with spectral density fθ(λ), where θ is an unknown parameter. The problem considered is that of testing a simple hypothesis H:θ = θ0 against the alternative A:θ ≠ θ0. For this problem we propose a class of tests S, which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the χ2 type asymptotic expansion of the distribution of T ∈ S up to order n-1, where n is the sample size. Also we derive the χ2 type asymptotic expansion of the distribution of T under the sequence of alternatives An: θ = θ0 + ε √n, ε{lunate} > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions.

本文言語English
ページ(範囲)494-511
ページ数18
ジャーナルJournal of Multivariate Analysis
27
2
DOI
出版ステータスPublished - 1988 11
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 数値解析
  • 統計学、確率および不確実性

フィンガープリント

「Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル