Hypothesis testing for mean vector and covariance matrix of multi-populations under a two-step monotone incomplete sample in large sample and dimension

In this study, we focus on the critical issue of analyzing data sets with missing data. Statistically processing such data sets, particularly those with general missing data, is challenging to express in explicit formulae, and often requires computational algorithms to solve. We specifically address monotone missing data, which are the simplest form of data sets with missing data. We conduct hypothesis tests to determine the equivalence of mean vectors and covariance matrices across different populations. Furthermore, we derive the properties of likelihood ratio test statistics in scenarios involving large samples and large dimensions.