Spherical Test Of Large Dimensional Data

In this paper,we study the spheroidal test of large-dimensional data.Using the Cauchy-Schwarz inequality,the test statistic?₁,?₂ is constructed by the ratio of the traces of the sample covariance matrix.First,we use the linear spectral statistic theory of the sample covariance ma-trix to obtain the asymptotic distribution of the statistic?₁,?₂ under the null hypothesis.Then,the asymptotic distribution of the?₁,?₂ statistic is corrected as necessary.In order to make the test statistic have higher test efficiency,the statistic?₁,?₂ normalized maximum value is selected as the test statistic?₁ in this paper.Compared to some existing test statistic,the statistic proposed in this paper has a relatively simple expression,and can process sample data with unknown mean and non-Gaussian population with general fourth moment.In addition,under the alternative hypothesis,when the population has a Spike structure,we obtain the the-oretical asymptotic potential function of the statistic under the alternative hypothesis.Finally,using Monte Carlo simulation,we have listed the empirical test level and test efficiency of the three test methods,such as?₁,CZZ test and FSG test.The results show that the proposed test statistic has good experience test level and test efficiency which performed.