Matching moments for a closer approximation of the weighted -divergence test statistics in goodness-of-fit for finite samples

The distributional properties of the weighted ( h , φ ) -divergence test statistics introduced in Landaburu and Pardo (2000) rely on large sample sizes for their validity. In this paper the accuracy of applying asymptotic results in cases where the sample size can not be assumed large is explored. In order to do this we compare the two asymptotic moments of the weighted ( h , φ ) -divergence test statistics with small-sample expressions for those moments.