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.
Acknowledgements
The authors would like to thank the referees for their helpful suggestions. The author Yo Sheena is grateful to the Department of Mathematics and Statistics, Bowling Green State University for providing him with wonderful research facilities.
Notes
On leave from Department of Economics, Shinshu University. Japan.