Large Deviation Local Limit Theorems for Ratio Statistics

Abstract

This document discusses an arbitrary sequence of non-lattice random variables and another sequence of positive random variables. Assume that the sequences are independent. This paper obtains asymptotic expression for the density function of the ratio statistic R sub n = T sub n/S sub n based on simple conditions on the moment generating functions of T sub n and S sub n. When S sub n = n, our main result reduces to that of Chaganty and Sethuraman. We also obtain analogous results when T sub n and S sub n are both lattice random variables. We call our theorems large deviation local limit theorems for R sub n, since the conditions of our theorems imply that R sub n approaches limit of c in probability for some constant c. We present some examples to illustrate our theorems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1988
Accession Number
ADA201169

Entities

People

  • Narasinga R. Chaganty
  • Sanjeev Sabnis

Organizations

  • Old Dominion University

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Communities of Interest

  • Air Platforms
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DTIC Thesaurus Topics

  • Classification
  • Data Science
  • Governments
  • Information Science
  • Integrals
  • Military Research
  • National Governments
  • Numbers
  • Probability
  • Probability Density Functions
  • Random Variables
  • Real Numbers
  • Security
  • Sequences
  • Statistical Analysis
  • Statistics
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Statistical inference.