Kurtosis Tests for Multivariate Normality with Monotone Incomplete Data

TL;DR

This paper develops a new kurtosis-based test for multivariate normality applicable to monotone incomplete data, deriving its distribution and demonstrating its use on cholesterol data.

Contribution

It introduces a generalized kurtosis statistic for monotone incomplete data and derives its asymptotic distribution under broad conditions.

Findings

The proposed test effectively detects deviations from multivariate normality.

Asymptotic distribution of the test statistic is established under broad conditions.

Application to cholesterol data illustrates practical utility.

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.