Improved parameter estimation for a family of exponential distributions

TL;DR

This paper introduces an improved parameter estimation method for a family of exponential distributions, generalizing the James--Stein approach, which outperforms classical methods under quadratic risk.

Contribution

It develops a generalized estimator for exponential distributions that dominates the maximum likelihood estimator, extending the James--Stein approach.

Findings

The new estimator outperforms MLE in simulations.

The method applies to various exponential distribution cases.

Numerical results confirm the estimator's superiority.

Abstract

In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed estimator dominates the classical maximum likelihood estimator under the quadratic risk. The estimating procedure is applied to special cases of distributions. The numerical simulations results are given.