Estimation of a multivariate normal covariance matrix under a certain structure

Abstract

We consider the estimation of Σ of the p-dimensional normal distribution Np (0, Σ) when Σ = θ0 Ip + θ1 aa′, where a is an unknown p-dimensional normalized vector and θ0 > 0, θ1 ≥ 0 are also unknown. First, we derive the restricted maximum likelihood (REML) estimator. Second, we propose a new estimator, which dominates the REML estimator with respect to Stein's loss function. Finally, we carry out Monte Carlo simulation to investigate the magnitude of the new estimator's superiority. On leave from Department of Economics, Shinshu University. Japan.