ASYMPTOTIC PROPERTIES OF THE GOODNESS-OF-FIT TESTS BASED ON SPACINGS

The Pitman's and Bahadur's asymptotic efficiencies of the goodness-of-fit tests based on higher-order non-overlapping spacings have been considered in the literature. This paper is concerned with the asymptotic intermediate efficiency due to Kallenberg of such tests. Particularly, it is shown that the Kallenberg's intermediate efficiencies of the statistics satisfying the Cramer's condition coincide with its Pitman's asymptotic efficiencies. Also it is shown that Greenwood's test known as optimal in Pitman's asymptotic efficiency sense is still optimal in Kallenberg's asymptotic weak intermediate efficiency sense.