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Displaying similar documents to “On the maximum term of a class of integral functions and its derivatives”

Approximate maximum likelihood estimation for a spatial point pattern.

Jorge Mateu, Francisco Montes (2000)

Qüestiió

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Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate for a spatial point pattern. This approximation is necessary because of the difficulty of evaluating the normalizing constant. However, it appears to be neither a general theory which provides grounds for preferring a particular method, nor any extensive empirical comparisons. In this paper, we review five general methods based on approximations to the maximum likelihood estimate...

A note on the existence of the maximum likelihood estimate in variance components models

Mariusz Grządziel, Andrzej Michalski (2014)

Discussiones Mathematicae Probability and Statistics

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In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML...

On the Jensen-Shannon divergence and the variation distance for categorical probability distributions

Jukka Corander, Ulpu Remes, Timo Koski (2021)

Kybernetika

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We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon...