Abstract

this article, we consider in more depth the effects of restricting the support of the distribution to the observed data values. This restriction has changed the problem from an infinite-dimensional one of maximizing over all continuous distributions to one of dimension n \Gamma 1. The restricted problem is analogous to allocating probabilities to each of n cells in a contingency table, where a single data point has been observed in each cell. The optimal probability allocation is arrived at as an adjustment of the the expected counts per cell chosen to minimize some goodness-of-fit criterion subject to constraints. In the case of empirical likelihood for the mean, the goodness of fit criterion is \Gamma2

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