Hotelling's one-sample and two-sample \(T^2\) tests and the multivariate Behrens-Fisher problem under nonnormality

DOI10.1016/j.jspi.2006.04.020zbMath1147.62019OpenAlexW2027380026MaRDI QIDQ947242

Yoshihide Kakizawa, Toshiya Iwashita

Publication date: 29 September 2008

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2006.04.020

zbMATH Keywords

asymptotic expansiondifferential operatorBehrens-Fisher problemlocal powernonnormalityHotelling's \(T^{2}\) statisticnonnull distribution

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Hypothesis testing in multivariate analysis (62H15) Functions of several variables (26B99)

Related Items (7)

Hotelling's \(T^2\) in separable Hilbert spaces ⋮ Improved chi-squared tests for a composite hypothesis ⋮ A modified two-factor multivariate analysis of variance: asymptotics and small sample approxi\-mations ⋮ Exact distribution of a modified Behrens–Fisher statistic ⋮ A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions ⋮ Multiple comparisons of several heteroscedastic multivariate populations ⋮ Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions

Cites Work

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• On the validity of the formal Edgeworth expansion
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• Asymptotic expansion of the joint distribution of sample mean vector and sample covariance matrix from an elliptical population
• An application of Lévy's inversion formula for higher order asymptotic expansion
• The exact distributions of the univariate and multivariate behrens-fisher statistics with a comparison of several solutions in the univariate case
• Asymptotic Formulae for the Distribution of Hotelling's Generalized $T^2_0$ Statistic
• A chain rule for differentiation with applications to multivariate hermite polynomials
• A modified score test statistic having chi-squared distribution to order n⁻¹
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• Higher order monotone Bartlett-type adjustment for some multivariate test statistics
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• An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic Expansion
• AN ASYMPTOTIC EXPANSION OF THE EXPECTATION OF THE ESTIMATED ERROR RATE IN DISCRIMINANT ANALYSIS1
• An Asymptotic Expansion of the Non-Null Distribution of Hotelling's Generalized $T_0^2$-Statistic
• An Asymptotic Expansion for the Distribution of the Linear Discriminant Function
• The bootstrap and Edgeworth expansion
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