Accession Number : ADA117513

Title :   Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Variables.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Chaganty,Narasinga Rao ; Sethuraman,J.

Report Date : JUN 1982

Pagination or Media Count : 39

Abstract : The results of W. Richter (Theory Prob. Appl. (1957) 2 206-219) on sums of independent, identically distributed random variables are generalized to arbitrary sequences of random variables Tn. Under simple conditions on the cumulant generating function of Tn, which imply that Tau n/n converges to o, it is shown, for arbitrary sequences (mn) converging to o, that kn(mn), the probability density function of Tn/n at mn, is asymptotic to an expression involving the large deviation rate of Tn/n. Analogous results for lattice random variables are also given. Applications of these results to statistics appearing in nonparametric inference are presented. (Author)

Descriptors :   *Random variables, *Sequences(Mathematics), Theorems, Probability density functions, Asymptotic series, Nonparametric statistics, Laplace transformation, Convergence

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE