Statistical inference of semidefinite programming
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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.
KeywordsSemidefinite programming Minimum trace factor analysis Matrix completion problem Minimum rank Nondegeneracy Statistical inference Asymptotics
Mathematics Subject Classification62F12 62F30 90C22
The author is indebted to anonymous referees for constructive comments which helped to improve the manuscript.
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