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- W2896873564 abstract "We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be applied in statistics, for example in the estimation of unknown covariance structures under the multi-level multivariate models, where positive definiteness is required. We conduct simulation studies to compare statistical properties of the estimators obtained by projection on the cone with a given matrix dimension and on the asymptotic cone." @default.
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- W2896873564 date "2018-05-16" @default.
- W2896873564 modified "2023-09-26" @default.
- W2896873564 title "On Projection of a Positive Definite Matrix on a Cone of Nonnegative Definite Toeplitz Matrices" @default.
- W2896873564 doi "https://doi.org/10.13001/1081-3810.3750" @default.
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