Statistical inference of semidefinite programming

Abstract

In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the ‘true’ covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider asymptotics of the so-called minimum trace factor analysis. We also discuss the minimum rank matrix completion problem and its SDP counterparts.