A BHEP test for multivariate normality on incomplete data

Abstract

A BHEP test for the null hypotesis of multivariate normality on the basis of incomplete data is introduced. Estimators for the underlying unknown parameters in this situation are suggested. The test uses characteristic functions and circumvents the problem of singular covariance matrix estimates. As the sample size tends to infinity, an almost sure limit of the test statistic is obtained under the null hypothesis and under alternatives. The convergence in distribution under the null hypothesis is also proved. Critical values can be obtained using a bootstrap procedure. Simulation studies investigate size and power of the test and confirm the adequacy of the approach. A real data example demonstrates the application of the test.