RENYI TYPE GOODNESS-OF-FIT TESTS WITH ADJUSTED PRINCIPAL DIRECTION OFALTERNATIVES

In the present paper we investigate the power of (weighted) Renyl test s in the sense of Gill (1980). The methods are based on a reparametriz ation of the underlying non-parametric problem in terms of hazard rate s which is inspired by survival analysis. Within this set-up, local as ymptotic normality (LAN) is established via martingale methods. Moreov er, following the approach of Milbrodt & Strasser (1990), it is shown that the power functions admit a principal components' decomposition o f their curvature at the hypothesis. As a consequence, consistency and asymptotic admissibility are obtained. In addition, for any given dir ection of alternatives, the Renyl tests may be adapted by choosing the ir weight function such that they are most sensitive against these alt ernatives. As applications we construct consistent counterparts of the two-sided Wilcoxon test and Savage test for two-sample testing proble ms, the latter being adjusted to proportional hazard rates models.