Stochastic dominance and parameter estimation: The case of symmetric stable distributions

Stochastic dominance rules can be applied to the selection of statistical estimators. This paper applies the procedure to estimators of location parameters of stable distributions: the mean and the median. It was found that the preference of one estimator over another depends on the characteristic exponent and on the sample size. Furthermore for some combinations of characteristic exponents and sample size we found that the stochastic dominance rule yields no preference implying that depending on one's utility function one may prefer the mean over the median or vise versa. This result differs from the common mean squared error criterion.