Estimation of the multivariate normal covariance matrix under some restrictions

Yo Sheena and Arjun K. Gupta

Abstract

We consider the estimation of Σ of the p-dimensional normal distribution Np(0,Σ) under the restriction where the eigenvalues of Σ have an upper or lower bound. From a decision-theoretic point of view, we evaluate the performance of the REML (restricted maximum likelihood estimator) with Stein′s loss function and propose another estimator that dominates the REML.

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Statistics & Risk Modeling publishes articles that discuss modern methods of statistics and probabilistic modeling and their applications to risk management in finance, insurance, and related areas. It also welcomes papers that present methodological innovations in statistical theory as well as papers on innovative statistical modeling applications and inference in risk management.

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