Statistical inference for multinomial populations based on a double index family of test statistics

Abstract

ABSTRACTIn the present work, we consider parameter estimation and hypothesis testing based on a general class of measures, namely the -power divergence family for multinomial populations. In particular, we propose a general family of double index -test statistics that involves two indices, the values of which play a key role in the effectiveness and accuracy of the proposed methodology. The asymptotic properties of the associated estimators are examined together with the power of the test and the asymptotic distribution under the contiguous alternatives. Finally, we explore through extensive simulations, the effect of the shape of the multinomial distribution on the performance of the proposed test.