Estimating Multinomial Probabilities
作者:
S. Kunte,
K.S. Upadhya,
期刊:
The American Statistician
(Taylor Available online 1996)
卷期:
Volume 50,
issue 3
页码: 214-216
ISSN:0003-1305
年代: 1996
DOI:10.1080/00031305.1996.10474382
出版商: Taylor & Francis Group
关键词: Bayes estimators;Laplace's law of succession;Multinomial probabilities
数据来源: Taylor
摘要:
Classical maximum likelihood (ML) as well as the uniformly minimum variance unbiased (UMVU) estimators of multinomial cell probabilities are given by the observed relative frequencies. Bayes estimators corresponding to symmetric Dirichlet prior distribution for p are the inflated observed relative cell frequencies of the type (ni+k) (M+kt)−1. These estimators, which are more reasonable when the observedni's are 0 or very small, are justified classically by Johnson and are also reported without proof in Good. We give here a proof of Johnson's results that perhaps is easier to understand.
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