Kurtosis tests for multivariate normality with monotone incomplete data

Abstract

We consider the problem of testing multivariate normality when the data consists of a random sample of two-step monotone incomplete observations. We define for such data a generalization of Mardia's statistic for measuring kurtosis, derive the asymptotic non-null distribution of the statistic under certain regularity conditions and against a broad class of alternatives, and give an application to a well-known data set on cholesterol measurements.

A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function

“…señor-Alva and Estrada (2009), Voinov et al (2016), Yanada et al (2015), and Zhou and Shao (2014), there is an ongoing interest in the problem of testing for multivariate normality. Without claiming to be exhaustive, the above list probably covers most of the publications in this field since the review paper Henze (2002).…”

Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample

“…As explained by Yamada et al [12], it is also assumed that data are randomly missing; it is necessary to assume that their absence is completely random in order to derive the maximum likelihood estimatorsμ k andˆ k .…”

“…H 01 : 1 = · · · = g , H 11 : H 01 is not valid, H 02 : µ 1 = · · · = µ g , 1 = · · · = g , H 12 : H 02 is not valid, H 03 : µ 1 = · · · = µ g , H 13 : H 03 is not valid, where µ i and i are the population mean vector and population covariance matrix, respectively, of the group i. We derive the likelihood ratio criterion and the Wald-type criterion using the maximum likelihood estimator or the unbiased estimator by Tsukada [11].…”

Asymptotic Properties for the Eigenvalue and Eigenvector of a Covariance Matrix under Two-Step Monotone Incomplete Multivariate Normal Data

“…In the content of the two-step monotone incomplete sample, the maximum likelihood estimator (MLE) of l and R is explicitly defined by Anderson and Olkin (1985), and the unbiased estimator (UBE) of R is derived by Tsukada (2014) and Hyodo, Shutoh, Seo, and Pavlenko (2016) as a closed form. Richards (2009, 2010) discussed the properties of the MLE, and Richards and Yamada (2010) obtained the Stein estimator of l. Yamada, Romer, and Richards (2015) proposed the normality test using kurtosis. Yagi and Seo (2015) studied the tests and simultaneous condence intervals for mean vectors in multi-samples.…”