Author(s)

Alex Samuel Mungo, Victor Mooto Nawa

School of Natural Sciences, University of Zambia, Lusaka, Zambia.

The study explores the asymptotic consistency of the James-Stein shrinkage estimator obtained by shrinking a maximum likelihood estimator. We use Hansen’s approach to show that the James-Stein shrinkage estimator converges asymptotically to some multivariate normal distribution with shrinkage effect values. We establish that the rate of convergence is of order  and rate , hence the James-Stein shrinkage estimator is -consistent. Then visualise its consistency by studying the asymptotic behaviour using simulating plots in R for the mean squared error of the maximum likelihood estimator and the shrinkage estimator. The latter graphically shows lower mean squared error as compared to that of the maximum likelihood estimator.

Asymptotic, Consistency, Convergence, Efficiency, Mean Squared Error, Shrinkage

Mungo, A. and Nawa, V. (2023) Asymptotic Consistency of the James-Stein Shrinkage Estimator. Open Journal of Statistics, 13, 872-892. doi: 10.4236/ojs.2023.136044.