Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Variables.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1982
- Accession Number
- ADA117513
Entities
People
- Jayaram Sethuraman
- Narasinga Rao Chaganty
Organizations
- Florida State University