Abstract
The likelihood ratio method for dealing with change-point problems of Yakir and Pollak (Citation1998), 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.
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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