TITLE:
Asymptotic Consistency of the James-Stein Shrinkage Estimator
AUTHORS:
Alex Samuel Mungo, Victor Mooto Nawa
KEYWORDS:
Asymptotic, Consistency, Convergence, Efficiency, Mean Squared Error, Shrinkage
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.6,
December
20,
2023
ABSTRACT: 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 orderand 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.