An asymptotic expansion for the distribution of Hotelling's \(T^ 2\)-statistic under nonnormality

DOI10.1006/jmva.1997.1668zbMath0873.62017OpenAlexW2060813903MaRDI QIDQ1361807

Yasunori Fujikoshi

Publication date: 4 November 1997

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.1997.1668

zbMATH Keywords

asymptotic expansioncharacteristic functionnonnormalityexplicit Edgeworth expansionHotelling's T-square statisticmultivariate \(t\)-statistic

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20)

Related Items (26)

A formula to improve score test statistics ⋮ Some integrals involving multivariate Hermite polynomials: application to evaluating higher-order local powers ⋮ An asymptotic expansion of the distribution of Student's \(t\) type statistic under spherical distributions ⋮ Contributions to multivariate analysis by Professor Yasunori Fujikoshi ⋮ Sampling distributions associated with the multivariate t distribution ⋮ Theorems of Hausdorff-Young and Paley-Wiener type for Fourier transforms of rapidly decreasing functions ⋮ Asymptotic expansions of the null distributions of some test statistics for profile analysis in general distributions ⋮ High dimensional asymptotics for the naive Hotelling T² statistic in pattern recognition ⋮ Analyzing Mean Profiles of Nonnormal Populations ⋮ 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 ⋮ Hotelling's one-sample and two-sample \(T^2\) tests and the multivariate Behrens-Fisher problem under nonnormality ⋮ An asymptotic expansion of the distribution of Rao's \(U\)-statistic under a general condition ⋮ Linear transformations to symmetry ⋮ High-dimensional Edgeworth expansion of a test statistic on independence and its error bound ⋮ On the Distributions of some Test Statistics for Profile Analysis in Elliptical Populations ⋮ On some tests of the covariance matrix under general conditions ⋮ Asymptotic Expansions for the Distributions of Maximum and Sum of Quasi-Independent Hotelling'sT²Statistics Under Non Normality ⋮ Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions ⋮ Improved confidence regions for a mean vector under general conditions ⋮ A necessary power divergence-type family of tests for testing elliptical symmetry ⋮ Some necessary uniform tests for spherical symmetry ⋮ Approximation of the non-null distribution of generalized \(T^2\)-statistics ⋮ A Multivariate Two-Sample Mean Test for Small Sample Size and Missing Data ⋮ Asymptotic expansions for the distributions of multivariate basic statistics and one-way MANOVA tests under non-normality ⋮ An application of Lévy's inversion formula for higher order asymptotic expansion

Cites Work

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• Edgeworth expansion for Student's t statistic under minimal moment conditions
• On moment conditions for valid formal Edgeworth expansions
• On the validity of the formal Edgeworth expansion
• On the robustness of hotelling's T²-test anb distribution of linear and quadratic forms III sampling from a mixture of two mult11ariate normal populations
• An Asymptotic Expansion of the Distribution of Hotelling'sT²-Statistic Under General Distributions
• The bootstrap and Edgeworth expansion

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