DefinePK

Abstract

Let \(0=U_{0,n}\leq U_{1,n}\leq \ldots \leq U_{n,n}=1\) be an ordered sample from uniform [0,1] distribution \(D_{in}=U_{i,n}-U_{i-1,n}\), \(i=1,2,..,n\), \(n=1,2,\ldots\) , be their spacings,and let \(f_{1n},\ldots,f_{nn}\) be a set of measurable functions. In this paper theorems on the probabilities of deviations in the moderate zones for \(R_{n}D=f_{1n}(nD_{1n}, \ldots , f_{nn}(nD_{nn}\) are presented. Application of these results to study an intermediate efficiencies of the tests based on statistic \(R_{n}(D)\) are also considered.