Mean likelihood estimators

The use of {\it Mathematica} in deriving mean likelihood estimators is discussed. Comparisons between the maximum likelihood estimator, the mean likelihood estimator and the Bayes estimate based on a Jeffrey's noninformative prior using the criteria mean-square error and Pitman measure of closeness. Based on these criteria we find that for the first-order moving-average time series model, the mean likelihood estimator outperforms the maximum likelihood estimator and the Bayes estimator with a Jeffrey's noninformative prior. {\it Mathematica} was used for symbolic and numeric computations as well as for the graphical display of results. A {\it Mathematica} notebook is available which provides supplementary derivations and code from http://www.stats.uwo.ca/mcleod/epubs/mele The interested reader can easily reproduce or extend any of the results in this paper using this supplement.