A New Approach To Test One High Dimensional Mean Vector

Nowadays,with the rapid development of science and technology,people en-counter various problems of big data in their work and life,such as,transaction data of securities market,multimedia graphics and video data,biometric data,which are called high-dimensional data by statisticians.And people are increasingly concerned about how to deal with high-dimensional data.In statistics,we have found that the classical Hoteling's T~2 test has serious deficiencies when the data dimension is high.So we need to find new statistical methods to solve the problem.In this paper,we mainly study the test of the one high dimensional mean vector based on regularized Hoteling's T~2 statistics.We introduce a new approach to test one high dimensional mean vector for both the data dimension is much larger than the sample size and smaller than the sample size.The new approach does not require normal conditions in the relationship between the data dimension and sample size.The asymptotic mean and variance of this statistic are obtained under the condition that the sample dimension and the sample size tend to be infinite at the same time,and the ratio approaches a constant,and the asymptotic distribution is deduced.