Some Estimates Of The Traces Of High-dimensional Covariance Matrices

Nowadays,with the rapid development of science and technology,high dimen-sional data has gradually appeared in our field of vision,and it has also been applied in more and more fields,such as in biology and financial research.We found that a common feature of high-dimensional data in research is that the dimensionali-ty of the data is greater than the size of the sample.This is what we know as"large p,small n",which is prone to "dimensionality disaster" phenomenon,but"The dimensionality disaster" phenomenon often makes it difficult to estimate the high-dimensional covariance matrix.In fact,when we deal with high-dimensional data,we often need to study the high-dimensional covariance matrix of the sam-ple,which leads to the study of the estimation method of the high-dimensional covariance matrix has become an important issue.In this article,we will study the three estimation methods of high-dimensional covariance matrix traces from Bai and Saranadasa,Chen and Qin and Li and Chen,and propose our new estimation method.Here,we are studying the situation of a sample,and each data in the sam-ple is independent and identically distributed.We mainly study the expectations and variances of the four estimation methods through theory.In addition,we will use the R language to simulate the data.On the basis of the three structures of the covariance matrix,when the high-dimensional data obeys the normal distribution and Laplace distribution,the real value and estimated value of the expectation and variance of the trace of the high-dimensional covariance matrix are simulated,and through the comparison of simulation results,a better estimation method of the high-dimensional covariance matrix trace is obtained.