Maximum likelihood estimation for the multinomial distribution with infinite number of cells

Radhakrishna Rao, C. (1958) Maximum likelihood estimation for the multinomial distribution with infinite number of cells Sankhya, 20 . pp. 211-218. ISSN 0972-7671

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Abstract

Maximum likelihood (m. l.) estimate of the infinite multinomial distribution exists with probability 1 and is consistent under a simple condition on the cell probabilities. To prove the consistency of an m. l. estimate of a parameter it is necessary to assume that the parameter is a continuous function of the distribution. The existence of the m. l. estimates of parameters and their consistency is established slightly weaker that those assumed by earlier writers.

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