International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 1, Article ID 58738, 22 pages
doi:10.1155/IJMMS/2006/58738

The probability of large deviations for the sum functions of spacings

Abstract

Let 0=U0,n≤U1,n≤⋯≤Un−1,n≤Un,n=1 be an ordered sample from uniform [0,1] distribution, and Din=Ui,n−Ui−1,n, i=1,2,…,n; n=1,2,…, be their spacings, and let f1n,…,fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)=f1n(nD1n)+⋯+fnn(nDnn) are proved. Application of these theorems for determination of the intermediate efficiencies of the tests based on Rn(D)-type statistic is presented here too.