The Limit Theory Of The Spectral Of Two Types Of The Sample Covariance Matrices

In recent years, with the development of computer science, many subject areas have been facing the problems of high dimensional data analysis, the high dimensional data analysis is more and more important in modern science, such as stock market analysis.While the general dimension reduction method is used to solve the high dimensional data,we would still have to face a high dimensional problem. The theoretical research about the spectral distribution of random matrix is the research direction of mathematicians and statisticians, and the theoretical results have been widely applied in many research areas.The semicircular law and Marcenko-Pastar(MP)law are the basic research in the limiting spectral analysis of large dimension random matrices.In this paper, firstly, considering the orders of the rows and columns of the overlapping matrices is different, we study the limit theorem for linear eigenvalue statistics of sample covariance matrices, where we choose the Chebyshev polynomials of the first kind as the basis for the test function space. Secondly, we consider the limiting spectral distribution of a new random matrix model where the entries are dependent across both rows and columns. More precisely, the entries of the random matrix is a linear process. When both the size of the sample n and the dimension of random variable p tend to infinity such that the radio p/n?0,p2/n??, we study the problem of the empirical spectral distribution of the sample covariance matrix.