Robust Estimation Of Covariance Matrix Of Multivariate Longitudinal Data

This paper proposes a robust and efficient method to estimate the covariance matrix of multivariate longitudinal data.First,we adopt a new modified Cholesky decomposition method to parameterize the covariance matrix of multivariate longitudinal data.This approach of the modified Cholesky decomposition can automatically guarantee the positive definiteness of the covariance matrix.In order to improve the robustness of the estimation,based on a bounded exponential score function,we construct a set of robust estimating equations and give an iterative algorithm.Furthermore,we also propose robust smooththreshold estimating equations,which can select variable while estimating parameters.Under some regularity conditions,we prove that the estimated results have the consistency of variable selection and Oracle properties.There are five chapters in this article: Chapter 1 introduces the estimating methods,and their advantages as well as disadvantages of the existing two-dimensional or multivariate longitudinal data covariance matrix.Chapter 2 decomposes and models the covariance matrix of multivariate longitudinal data,and proposes a set of robust estimation equations to estimate the corresponding model parameters.In order to improve the robustness and efficiency of the estimation,we have also considered the problem of variable selection,and propose a robust smooth-threshold estimation method.Chapter 3 gives the asymptotic properties of the estimator in the model.Chapter 4 conducts numerical simulation research on the proposed robust estimation and variable selection methods.Chapter 5is mainly about the asymptotic properties of estimators,including concrete consistency,asymptotic normality and Oracle properties.