On the performance of estimators of parameter in autoregressive model of order one and optimal prediction under asymmetric loss

Abstract

In the AR(1) set-up it is well known that for different ranges of the parameter values the distribution of different quantities of interest (such as, the estimators, test statistics etc.) are different. As a result, the equal amount of over-estimation and under-estimation may not have the equal consequences. Thus the use of symmetric loss function in estimating the unknown parameter is not recommendable. Here we have shown that under asymmetric loss function Bayes' estimator outperforms the classical point estimator when the operational prior is sufficiently diffuse. Prediction problems involving asymmetric loss function arise in many fields. Optimal prediction problem will also be discussed using asymmetric loss function. It has been observed that the conditionally optimal predictor is biased under asymmetric loss and the amount of bias is also time varying in general.