Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

Abstract

In this study, a biased estimator is proposed for the scale parameter of Laplace distribution. First, it is theoretically shown that the mean square error of the biased estimator is smaller than that of the maximum likelihood estimator. Then the maximum likelihood estimator is compared with the obtained biased estimator by means of a simulation study using the relative efficiency of these estimators. In addition, confidence intervals are constructed for the scale parameter of Laplace distribution with bootstrap method in order to compare them with each other in a different way.