Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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BIC is strongly consistent for the pseudo-true factor order in misspecified exploratory factor analysis when optimal models share a common covariance set, the Gaussian criterion has a local quadratic margin, and complexity penalties are order-separating.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Consistency of the Bayesian Information Criterion for Model Selection in Exploratory Factor Analysis
BIC is strongly consistent for the pseudo-true factor order in misspecified exploratory factor analysis when optimal models share a common covariance set, the Gaussian criterion has a local quadratic margin, and complexity penalties are order-separating.