Accuracy Borrowing in the Estimation of the Mean by Shrinkage to an Interval
- 1 September 1968
- journal article
- research article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 63 (323) , 953-963
- https://doi.org/10.1080/01621459.1968.11009322
Abstract
The topic of the shrinkage of an estimator for the mean of a normal distribution towards a point ([3] Thompson) is extended to shrinkage to an interval centered at μ = 0. An effort is made to keep the form of the modified estimator relatively simple, while obtaining more flexibility than is possessed by the sample mean . The family of estimators advocated is: Curves of MSE/σ (where MSE is mean square error) versus |μ/ | are given for a number of values of θ and κ. A table is given by the use of which κ and θ may be selected on the basis of the minimum value of MSE/σ , the width of the interval for which MSE/σ < 1, the maximum value of MSE/σ , and the value of |μ/ | for which MSE/σ is a maximum.Keywords
This publication has 3 references indexed in Scilit:
- Some Shrinkage Techniques for Estimating the MeanJournal of the American Statistical Association, 1968
- Some Applications of the Cramer-Rao InequalityPublished by University of California Press ,1951
- On the convergence of quadrature formulas related to an infinite intervalTransactions of the American Mathematical Society, 1928