Estimating High-dimensional Covariance and Precision Matrices under General Missing Dependence

Abstract

A sample covariance matrix S of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis, and testing of equality of mean vectors. However, when the data are partially observed, the sample covariance matrix from the available data is biased and does not provide valid multivariate procedures.To correct the bias, a simple adjustment method called inverse probability weighting (IPW) has been used in previous research, yielding the IPW estimator. The estimator plays the role of S in the missing data context so that it can be plugged into offthe-shelf multivariate procedures. However, theoretical properties (e.g. concentration) of the IPW estimator have been only established under very simple missing structures; every variable of each sample is independently subject to missing with equal