Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes

Masanobu Taniguchi*

*この研究の対応する著者

研究成果: Article査読

11 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. To estimate θ we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let θ̂τ be the minimum contrast estimator of θ. Then we derive the Edgewroth expansion of the distribution of θ̂τ up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.

本文言語English
ページ(範囲)1-28
ページ数28
ジャーナルJournal of Multivariate Analysis
21
1
DOI
出版ステータスPublished - 1987 2
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

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