Research On The Estimation Of High-dimensional Dynamic Covariance Model

The rapid development of big data has caused high-dimensional data widely used in statistical research.One of the most obvious feature of this high-dimensional data set is that the relationship between the variables is very complicated.Therefore,how to understand the structure of the data set is an important statistical problem.Many statistical analyses concentrate on the estimation of the covariance matrix or its inverse(precision matrix).Related work has focused on the static model where the covariance matrix is independent of the time.In this case,the dimension of the data is usually p,It is much larger than the sample size n,but in many practical applications,the paired relationship between these variables changes with changes in many factors:such as fMRI data and financial time,In series data,the relationship between variables in the data will change with time,and this change cannot be reflected in the static model.In response to this problem,a recent article proposed a type of dynamic covariance hypothesis as sparse conditions.The model(DCM)uses the POET method to estimate the model,and studies the uniform convergence rate of the method.Compared with the static model,the model can be applied to more complex situations.This article is based on the existing POET method.Improved,in the non-parametric method of estimating the conditional covariance matrix,the Nadaraya-Watson estimation is replaced by a local linear estimation,and the convergence speed is extended from the compact support to the infinite interval.Finally,the model Carlo simulation and Chen(2016)The proposed estimation results are compared,and the experimental results show that the method in this paper has better estimation results and stronger robustness in many cases.