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.