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James, W. and Stein, C. (1961) Estimation with Quadratic Loss. In: Neyman, J., ed., Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Statistical Laboratory of the University of California, Berkeley.

has been cited by the following article:

• 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.