Shrinkage estimation for square of location parameter of the exponential distribution with known coefficient of variation

Shrinkage estimation has become a basic tool in the computational analysis of highdimensional data. Historically and conceptually a key development toward this was the discovery of the inadmissibility of the usual estimator of a multivariate normal mean. This study explores the problem of estimating the square of location parameter of an exponential distribution when the coefficient of variation is known without error. Several estimators have been proposed with their properties. The best unbiased estimator as well least minimum mean square error (MMSE) estimator has been identified among several estimators. Numerical illustrations are given in the support of the present study.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

Shrinkage estimation is a fundamental tool in analyzing high-dimensional data. This study focuses on estimating the square of the location parameter in an exponential distribution when the coefficient of variation is known without error. Various estimators are proposed and compared, and the best unbiased estimator and the minimum mean square error estimator are identified. Numerical illustrations are provided to support the findings of this study.