Pilot estimators for a kind of sparse covariance matrices with incomplete heavy-tailed data

Abstract

This paper investigates generalized pilot estimators of covariance matrix in the presence of missing data. When the random samples have only bounded fourth moment, two kinds of generalized pilot estimators are provided, the generalized Huber estimator and the generalized truncated mean estimator. In addition, we construct thresholding generalized pilot estimator for a kind of sparse covariance matrices and establish the convergence rates in terms of probability under spectral and Frobenius norms respectively. Moreover, the convergence rates in sense of expectation are also given under an extra condition. Finally, simulation studies are conducted to demonstrate the superiority of our method.

Keywords

• sparse covariance matrix
• incomplete data
• generalized pilot estimator
• convergence rate