A Robust Test Statistic for Independence in High Dimensional Data

Abstract

The likelihood ratio test used to test complete independence cannot be used in high-dimensional data. In literature, many test statistics were proposed to cope with this problem. However, these statistics are sensitive to outliers. In this study, we suggest a test statistic that is not sensitive to outliers and can be used in high-dimensional data to test complete independence. We investigate the performance of our suggested statistic in terms of the empirical size and the empirical power by using three simulation studies and a real example dataset. And, we construct an R package to implement our proposed test statistic on real high-dimensional data in applications.