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Error Bounds and Improved Probability Estimation using the Maximum Likelihood Set (2007)
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@MISC{Karakos07errorbounds,
author = {Damianos Karakos and Sanjeev Khudanpur},
title = {Error Bounds and Improved Probability Estimation using the Maximum Likelihood Set},
year = {2007}
}
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Abstract
Abstract — The maximum likelihood set (MLS) is a novel candidate for nonparametric probability estimation from small samples that permits incorporating prior or structural knowledge into the estimator [1]. It is a set of probability distributions which assign to the observed type (or empirical distribution) a likelihood that is no lower than the likelihood they assign to any other type. The MLS has been shown to have many highly desirable properties, including strong consistency of MLS-based estimates; yet the probability that the MLS contains the data-generating distribution may be arbitrarily small! In this paper, we propose to overcome this shortcoming via an ε-fattening of the MLS. The proposed set, called the High Likelihood Set (HLS), with ε → 0 slowly in sample size, ensures that the HLS contains the datagenerating distribution with arbitrarily large probability, while retaining most desirable properties of the MLS. In particular, the
Keyphrases
improved probability estimation error bound maximum likelihood set desirable property small sample empirical distribution structural knowledge sample size mls-based estimate novel candidate large probability probability distribution high likelihood set data-generating distribution maximum likelihood nonparametric probability estimation strong consistency
