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

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