Estimation of the covariance matrix with two-step monotone missing data

Abstract

We suggest shrinkage based technique for estimating covariance matrix in the high-dimensional normal model with missing data. Our approach is based on the monotone missing scheme assumption, meaning that missing values patterns occur completely at random. Our asymptotic framework allows the dimensionality p grow to infinity together with the sample size, N, and extends the methodology of Ledoit and Wolf (2004) Ledoit, O., Wolf, M. (2004). A well-conditioned estimator for large dimensional covariance matrices. J. Multivariate Anal. 88:365–411.Crossref], Web of Science ®] , Google Scholar] to the case of two-step monotone missing data. Two new shrinkage-type estimators are derived and their dominance properties over the Ledoit and Wolf (2004) Ledoit, O., Wolf, M. (2004). A well-conditioned estimator for large dimensional covariance matrices. J. Multivariate Anal. 88:365–411.Crossref], Web of Science ®] , Google Scholar] estimator are shown under the expected quadratic loss. We perform a simulation study and conclude that the proposed estimators are successful for a range of missing data scenarios.