The probability of large deviations for the sum functions of spacings

Sherzod Mira'zam Mirakhmedov

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-22

Abstract:

Let 0 = U 0 , n ≤ U 1 , n ≤ ⋯ ≤ U n − 1 , n ≤ U n , n = 1 be an ordered sample from uniform [ 0 , 1 ] distribution, and D i n = U i , n − U i − 1 , n , i = 1 , 2 , … , n ; n = 1 , 2 , … , be their spacings, and let f 1 n , … , f n n be a set of measurable functions. In this paper, the probabilities of themoderate and Cramer-type large deviation theorems for statistics R n ( D ) = f 1 n ( n D 1 n ) + ⋯ + f n n ( n D n n ) are proved. Application of these theorems for determination of theintermediate efficiencies of the tests based on R n ( D ) -type statistic is presented here too.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:058738

DOI: 10.1155/IJMMS/2006/58738

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