Tail Approximations for Maxima of Random Fields by Likelihood Ratio Transformations

Abstract

The likelihood ratio method for dealing with change-point problems of Yakir and Pollak (1998), which has subsequently been extended to deal with a wide variety of problems involving maxima of random fields, has as a key ingredient a conditional local limit theorem for a log-likelihood ratio, given an almost independent “local” sigma-algebra. This article contains a general version of that theorem, illustrated by several examples.

Keywords:

• Change of measure
• Change-point
• Likelihood ratio
• Local limit theorem

Subject Classification:

• Primary 62L15
• Secondary 60G40

ACKNOWLEDGMENTS

This research has been supported by the US National Science Foundation and by the Israel–US Binational Science Foundation Grant 2006101.

Notes

Recommended by A. G. Tartakovsky