Estimation of Multinomial Probabilities.
CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES
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This paper deals with the estimation of the parameters cell probabilities of a multinomial distribution. The maximum likelihood estimator MLE is known to be minimax and admissible with respect to a quadratic loss function. It is shown that the MLE is admissible with respect to a non-quadratic loss function. For the parameters of m multinomial distributions being estimated simultaneously and the loss being quadratic, an estimator is given which is shown to have smaller risk than the MLE for all but a small subset of the parameter space, when m is large. Author
- Statistics and Probability