PROBABILITY OF THE MODERATE DEVIATIONS FOR THE SUM-FUNCTIONS OF SPACINGS

Let 0 = U0;n ≤U1;n ≤ … Un-1;n≤Un;n = 1 be an ordered sample from uniform [0,1] distribution,Din = Ui;n – Ui-1,n, i = 1; 2,…n; n = 1; 2; …; be their spacings,and let f1n; …; fnnbe a set of measurable functions. In this paper theorems on the probabilities of deviations in the moderate zones for Rn(D) = f1n(nD1n;+… + fnn(nDnn are presented. Application of these results to study an intermediate efficiencies of the tests based on statistic Rn(D) are also considered.