Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality

Wakaki, Hirofumi; Yanagihara, Hirokazu; Fujikoshi, Yasunori

doi:10.32917/hmj/1151007641

Cited by 20 publications

(19 citation statements)

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“…This is the reason why the correction by bootstrapping becomes poor when p is large. Therefore, EIC should not be used so often when dimension p is large in comparison with sample size n. The same results for the bootstrap method in a multivariate model were reported in Fujikoshi et al [5] and Wakaki et al [13].…”

Section: Resultssupporting

confidence: 55%

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

Yanagihara

2006

Journal of Multivariate Analysis

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This paper deals with the bias reduction of Akaike information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. We propose a corrected version of AIC which is partially constructed by the jackknife method and is adjusted to the exact unbiased estimator of the risk when the candidate model includes the true model. It is pointed out that the influence of nonnormality in the bias of our criterion is smaller than the ones in AIC and TIC. We verify that our criterion is better than the AIC, TIC and EIC by conducting numerical experiments.

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Section: Resultssupporting

confidence: 55%

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

Yanagihara

2006

Journal of Multivariate Analysis

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“…There are also a few recent works on asymptotic expansions of the distributions of these statistics under non-normality (Fujikoshi 2002;Wakaki et al 2002;Kakizawa 2009). Despite its theoretical as well as practical importance, the more general case without the assumption of constant covariance matrix has received only little attention.…”

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confidence: 98%

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Harrar

Bathke

2010

Ann Inst Stat Math

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In this paper, we present results for testing main, simple and interaction effects in heteroscedastic two factor MANOVA models. In particular, we suggest modifications to the MANOVA sum of squares and cross product matrices to account for heteroscedasticity. Based on these modified matrices, we define some multivariate test statistics and derive their asymptotic distributions under non-normality for the null as well as non-null cases. Derivation of these results relies on the perturbation method and limit theorems for independently distributed random matrices. Based on the asymptotic distributions, we devise small sample approximations for the quantiles of the null distributions. The numerical accuracy of the large sample as well as small sample approximations are favorable. A real data set from a Smoking Cessation Trial is analyzed to illustrate the application of the methods.

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“…340-342), though their distribution can be moderately affected by skewness or kurtosis when the sample size is small (Kano, 1995;Wakaki, Yanagihara, & Fujikoshi, 2002).…”

Section: Distribution Violationsmentioning

confidence: 97%

Mean Comparison: Manifest Variable Versus Latent Variable

Yuan

Bentler

2006

Psychometrika

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Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality

Cited by 20 publications

References 20 publications

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Mean Comparison: Manifest Variable Versus Latent Variable

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