A Study on LINEX Loss Function with Different Estimating Methods

摘要

LINEX means linearexponential loss function which used in the analysis of statistical estimationand prediction problem which rises exponentially on one side of zero and almostlinearly on the other side of zero. It is used in both overestimation and underestimationproblems. Ali Shadrokh and Hassan Pazira [1] presented Shrinkage estimator in Gamma Type-II Censored Dataunder LINEX loss function. In that paper, they have explainedhow the LINEX loss function works however no practical or detail explanationswere given in terms of changing the shape parameter and the error function. Inthis study we have explained how the LINEX loss function works throughpractical or detail explanations in terms of changing the shape parameter andthe error function, also see how the lossfunction works with the data generated from gamma distribution throughresampling methods to compare the performance of LINEX loss function consideringthe relative estimation error and usual estimation error through generatingrandom numbers from gamma distribution like randomization method and by usingbootstrapping samples. The very intention isto find out which resampling method performs well in using the LINEX loss function. Using Monte CarloSimulations these estimators are compared. It is doing draw random number fromthe gamma distribution and finds themaximum likelihood estimate of θ is  and using this estimatorto explain the LINEX loss function ; , or , where c isthe shape parameter and  is any estimate of the parameter . The shape of this loss function is determined by the valueof c. In the analysis we use the values of shape parameter c = -0.25, -0.50, -0.75, -1and c = 0.25, 0.50, 0.75, 1. The sameprocedure is done by using bootstrapping method, and finally compared between this two methods. Therelative estimation error should be used instead of the estimation error wherethe LINEX loss function works better in both of the cases. Between the twoestimators, bootstrap method is better work because although thecharacteristics are same, bootstrap method is more dispersed thanothers.