Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches

In this paper, we give the most current account of methods for comparison of populations or treatment groups with high-dimensional data. We conveniently group the methods into three categories based on the hypothesis of interest and the model assumptions they make. We offer some perspectives on the connections and distinctions among the tests and discuss the ramifications of the model assumptions for practical applications. Among other things, we discuss the interpretation of the hypotheses and results of the appropriate tests and how this distinguishes the methods in terms of what data type they are suitable for. Further, we provide a discussion of computational complexity and a list of available R-packages implementations and their limitations. Finally, we illustrate the numerical performances of the various tests in a simulation study.