Higher order asymptotic theory for normalizing transformations of maximum likelihood estimators

Masanobu Taniguchi, Madan L. Puri

研究成果: Article

5 引用 (Scopus)

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Suppose that Xn=(X1,... Xn) is a collection of m-dimensional random vectors Xi forming a stochastic process with a parameter θ{symbol}. Let {Mathematical expression} be the MLE of θ{symbol}. We assume that a transformation A( {Mathematical expression}) of {Mathematical expression} has the k-thorder Edgeworth expansion (k=2,3). If A extinguishes the terms in the Edgeworth expansion up to k-th-order (k≥2), then we say that A is the k-th-order normalizing transformation. In this paper, we elucidate the k-th-order asymptotics of the normalizing transformations. Some conditions for A to be the k-th-order normalizing transformation will be given. Our results are very general, and can be applied to the i.i.d. case, multivariate analysis and time series analysis. Finally, we also study the k-th-order asymptotics of a modified signed log likelihood ratio in terms of the Edgeworth approximation.

元の言語English
ページ(範囲)581-600
ページ数20
ジャーナルAnnals of the Institute of Statistical Mathematics
47
発行部数3
DOI
出版物ステータスPublished - 1995 9 1
外部発表Yes

ASJC Scopus subject areas

  • Statistics and Probability

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