Transformations with improved chi-squared approximations

DOI10.1006/jmva.1999.1854zbMath0969.62012OpenAlexW2040346244MaRDI QIDQ1975526

Yasunori Fujikoshi

Publication date: 4 October 2001

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

Full work available at URL: https://doi.org/10.1006/jmva.1999.1854

zbMATH Keywords

asymptotic expansionsBartlett correctionmonotone transformationchi-squared approximation

Mathematics Subject Classification ID

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

Related Items (21)

Improvement of the test of independence among groups of factors in a multi-way contingency table ⋮ Contributions to multivariate analysis by Professor Yasunori Fujikoshi ⋮ A family of estimators for multivariate kurtosis in a nonnormal linear regression model ⋮ Asymptotic expansions of the null distributions of some test statistics for profile analysis in general distributions ⋮ Effect of nonnormality on tests for a mean vector with missing data under an elliptically contoured pattern-mixture model ⋮ Analyzing Mean Profiles of Nonnormal Populations ⋮ Improved simplified T² test statistics for a mean vector with monotone missing data ⋮ Transformed goodness-of-fit statistics for a generalized linear model of binary data ⋮ Transformed statistics for tests of conditional independence in \(J \times K \times L\) contingency tables ⋮ Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure ⋮ A modified Bartlett test for heteroscedastic one-way MANOVA ⋮ Unnamed Item ⋮ Some corrections of the score test statistic for Gaussian ARMA models ⋮ Improved transformed statistics for the test of independence in \(r\times s\) contingency tables ⋮ Three Approximate Solutions to the Multivariate Behrens–Fisher Problem ⋮ Bias correction forT²type statistic with two-step monotone missing data ⋮ Improved transformed deviance statistic for testing a logistic regression model ⋮ Asymptotic expansions of the distributions of some test statistics in generalized linear models ⋮ Improved confidence regions for a mean vector under general conditions ⋮ Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables ⋮ On the asymptotic distribution of \(T^2\)-type statistic with two-step monotone missing data

Cites Work

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• On the distributions of the Hotelling's \(T^ 2\)-statistics
• Approximations for the quantiles of Student's \(t\) and \(F\) distributions and their error bounds
• Improvement on chi-squared approximation by monotone transformation
• Approximations to noncentral distributions
• A GENERAL METHOD FOR APPROXIMATING TO THE DISTRIBUTION OF LIKELIHOOD RATIO CRITERIA
• Asymptotic Formulae for the Distribution of Hotelling's Generalized $T^2_0$ Statistic
• A modified score test statistic having chi-squared distribution to order n⁻¹
• On the level-error after Bartlett adjustment of the likelihood ratio statistic
• A Method for Improving the Large-Sample Chi-Squared Approximations to Some Multivariate Test Statistics
• Higher order monotone Bartlett-type adjustment for some multivariate test statistics
• ASYMPTOTIC APPROXIMATIONS OF THE NULL DISTRIBUTION OF THE ONE-WAY ANOVA TEST STATISTIC UNDER NONNORMALITY

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