Understanding Shrinkage Estimators: From Zero to Oracle to James-Stein

36 Pages Posted: 17 Oct 2015

See all articles by Eric Bennett Rasmusen

Eric Bennett Rasmusen

Indiana University - Kelley School of Business - Department of Business Economics & Public Policy

Date Written: October 17, 2015

Abstract

The standard estimator of the population mean is the sample mean, which is unbiased. Constructing an estimator by shrinking the sample mean results in a biased estimator, with an expected value less than the population mean. On the other hand, shrinkage always reduces the estimator's variance and can reduce its mean squared error. This paper tries to explain how that works. I start with estimating a single mean using the zero estimator and the oracle estimator, and continue with the grand-mean estimator. Thus prepared, it is easier to understand the James-Stein estimator, in its simple form with known homogeneous variance and in extensions. The James-Stein estimator combines the oracle estimate's coefficient shrinking with the grand mean estimator's cancelling out of overestimates and underestimates.

Keywords: James Stein estimator, shrinkage estimator, oracle estimator, admissibility

JEL Classification: C13

Suggested Citation

Rasmusen, Eric Bennett, Understanding Shrinkage Estimators: From Zero to Oracle to James-Stein (October 17, 2015). Kelley School of Business Research Paper No. 15-76. Available at SSRN: https://ssrn.com/abstract=2675681 or http://dx.doi.org/10.2139/ssrn.2675681

Eric Bennett Rasmusen (Contact Author)

Indiana University - Kelley School of Business - Department of Business Economics & Public Policy ( email )

Enter your address line 1 here
Enter your address line 2 here
Bloomington, IN Enter your state here 47405
United States
812-855-9219 (Phone)
812-855-3354 (Fax)

HOME PAGE: http://rasmusen.org

Register to save articles to
your library

Register

Paper statistics

Downloads
93
rank
271,881
Abstract Views
487
PlumX Metrics