A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

TL;DR

This paper reviews 20 years of naive significance tests for high-dimensional mean vectors and covariance matrices, emphasizing their simplicity, robustness, and potential for broad application in high-dimensional statistical testing.

Contribution

It provides a comprehensive overview of naive testing methods for high-dimensional data, highlighting their advantages and potential for widespread use.

Findings

Naive tests are simple and robust in high dimensions.

They are effective for testing high-dimensional mean vectors.

They have broad applicability in various high-dimensional testing problems.

Abstract

In this paper, we will introduce the so called naive tests and give a brief review on the newly development. Naive testing methods are easy to understand and performs robust especially when the dimension is large. In this paper, we mainly focus on reviewing some naive testing methods for the mean vectors and covariance matrices of high dimensional populations and believe this naive test idea can be wildly used in many other testing problems.