  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.
