Statistical Inference of Semidefinite Programming

Alexander Shapiro (ashapiroisye.gatech.edu)

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.

Keywords: Semidefinite Programming, Minimum Trace Factor Analysis, Matrix Completion problem, minimum rank, nondegeneracy, statistical inference, asymptotics

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Stochastic Programming

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Entry Submitted: 01/31/2017
Entry Accepted: 01/31/2017
Entry Last Modified: 09/25/2017

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