Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Varibles

Authors

Narasinga Rao Chaganty, Old Dominion UniversityFollow
J Sethuraman

Document Type

Article

Publication Date

1985

DOI

10.1214/aop/1176993069

Publication Title

Annals of Probability

Volume

13

Issue

1

Pages

97-114

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 T_n. Under simple conditions on the cumulant generating function of T_n, which imply that T_n/n converges to zero, it is shown, for arbitrary sequences {m_n}, that k_n (m_n), the probability density function of T_n/n at m_n, is asymptotic to an expression involving the large deviation rate of T_n/n. Analogous results for lattice random variables are also given. Applications of these results to statistics appearing in nonparametric inference are presented. Other applications to asymptotic distributions in statistical mechanics are pursued in another paper.

Comments

Web of Science: "Free full-text from publisher."

Original Publication Citation

Chaganty, N. R., & Sethuraman, J. (1985). Large deviation local limit theorems for arbitrary sequences of random variables. Annals of Probability, 13(1), 97-114. doi:10.1214/aop/1176993069

Repository Citation

Chaganty, Narasinga Rao and Sethuraman, J, "Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Varibles" (1985). Mathematics & Statistics Faculty Publications. 78.
https://digitalcommons.odu.edu/mathstat_fac_pubs/78