Third-order asymptomic properties of a class of test statistics under a local alternative

Masanobu Taniguchi*


研究成果: Article査読

32 被引用数 (Scopus)


Suppose that {Xi; i = 1, 2, ...,} is a sequence of p-dimensional random vectors forming a stochastic process. Let pn, θ(Xn), Xn ∈ Rnp, be the probability density function of Xn = (X1, ..., Xn) depending on θ ∈ Θ, where Θ is an open set of R1. We consider to test a simple hypothesis H : θ = θ0 against the alternative A : θ ≠ θ0. For this testing problem we introduce a class of tests S, which contains the likelihood ratio, Wald, modified Wald, and Rao tests as special cases. Then we derive the third-order asymptotic expansion of the distribution of T ∈ S under a sequence of local alternatives. Using this result we elucidate various third-order asymptotic properties of T ∈ S (e.g., Bartlett's adjustments, third-order asymptotically most powerful properties). Our results are very general, and can be applied to the i.i.d. case, multivariate analysis, and time series analysis. Two concrete examples will be given. One is a Gaussian ARMA process (dependent case), and the other is a nonlinear regression model (non-identically distributed case).

ジャーナルJournal of Multivariate Analysis
出版ステータスPublished - 1991 5月

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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