A note on Asymptotical Efficiency of the Goodness of Fit Tests Based on disjoint k-spacings Statistic

Abstract

In this paper Pitman's asymptotic efficiencies (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed.