Semi- Minimax Estimation of the Scale Parameter of Laplace Distribution under Symmetric and Asymmetric Loss Functions

摘要

In this paper, semi- minimax estimation of the scale parameter of Laplace distribution is presented by applying the theorem of Lehmann (1950) under symmetric (quadratic) and asymmetric (entropy and MLINEX) loss functions. The results of comparison among these estimators are compared empirically using R- Code simulation study with respect to the mean square error (MSE). In general, the result has showed that the semi- minimax estimator under MLINEX loss function is the best estimator with respect to MSE for all sample sizes. It has also observed that, MSE’s of the estimators is increasing with the increase of the scale parameter value. Finally, for all parameter values, an obvious reduction in MSE’s has observed with the increase in sample size.