Asymptotically Optimal Tests when Parameters are Estimated

Abstract

The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators enable us to achieve this end. Two particular cases, AR(1) and ARCH models were studied and the asymptotic power function was derived.