Abstract [3]

[Author] Hirokazu Yanagihara
[Title] Asymptotic expansions of the null distributions of three test
statistics in a nonnormal GMANOVA model.
[Journal] Hiroshima Mathematical Journal , (2001), Vol. 31, No. 2, 213-262.


This paper deals with three test statistics for testing a linear
hypothesis and estimators of regression coefficients in the in
the GMANOVA model which was proposed by Potthof and Roy
(Biometrika, 1964), without assuming normal error. The test
statistics considered include the likelihood ratio statistic, the
Lawley-Hotelling trace criterion and the Bartlett-Nanda-Pillai
trace criterion, which have been proposed under normality. We
obtain asymptotic expansions of the null distributions of three
test statistics up to the order n-1, where n is the sample size.
The results are generalizations of the formulas in Wakaki,
Yanagihara and Fujikoshi (Hiroshima Math. J., 2002). In addition,
asymptotic expansions of the distribution functions of several
standardized statistics on regression coefficients are derived.

Key Words : Asymptotic expansion, Confidence interval,
Conservativeness, General multivariate linear hypothesis,
GMANOVA model, Linear combination, MLE, Nonnormality,
Null distribution, Robustness.

Abstract (Japanese)

本論文は Potthof and Roy によって提案された一般化多変量分散分析モデル
(Biometrika, 1964) での線形仮説に対する三つの検定統計量の非正規性の下
での帰無分布の漸近展開に関係するものである. 扱った検定統計量は正規性
の下で導出された尤度比統計量, ローレイ=ホテリング トレース統計量, バートレ
ット=ナンダ=ピライ トレース統計量である. 今回, これら三つの検定統計量の帰
無分布の n-1 (n は標本サイズ) 項までの漸近展開を得た. この結果は Wakaki,
Yanagihara and Fujikoshi (Hiroshima Math. J., 2002) の漸近展開公式の一般化
になっている. 付け加えて, いくらかの基準化された回帰係数の推定量の分布関