Minimax Estimation of the Scale Parameter of Laplace Distribution under Squared-Log Error Loss Function

Abstract

In this paper, we obtained Minimax estimator of the scale parameter  for the Laplace distribution under the Squared log error loss function by applying the theorem of Lehmann [1950], and compared it with Minimax estimator under Quadratic loss function in addition of Maximum Likelihood Estimator according to Monte-Carlo simulation study. The performance of these estimators is compared depending on the mean squared errors (MSE’s).

Keywords: Minimax estimator, Laplace distribution, Bayes estimator, Squared-log error loss function, Jeffery prior, Mean squared error.