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Mean Likelihood Estimators

A. Ian McLeod
Organization: University of Western Ontario
Department: Department of Statistical and Actuarial Sciences
Journal / Anthology

Year: 1997

The use of Mathematica in deriving mean likelihood estimators is discussed with several examples. Comparison between the maximum likelihood estimator and the mean likelihood estimator are made using the mean-square error and the Pitman measure of closeness. It is shown that although mean likelihood and maximum likelihood are both first order efficient, the asymptotic Pitman measure of closeness may not necessarily be equal to 0.5. In the exponential case, the mean likelihood estimate has uniformly smaller mean-square error but uniformly poorer Pitman measure of closeness. On the other hand in the case of the binomial and MA(1) model, the mean likelihood generally outperforms the maximum likelihood estimate under both of these criteria. Mathematica was used for symbolic and numeric computations as well as for the graphical display of results and the original typeset version of this article.

*Mathematics > Probability and Statistics
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