ADAPTIVE CHOICE OF TRIMMING PROPORTIONS

We consider Jaeckel's (1971, Ann. Math. Statist., 42, 1540-1552) propo sal for choosing the trimming proportion of the trimmed mean in the mo re general context of choosing a trimming proportion for a trimmed L-e stimator of location. We obtain higher order expansions which enable u s to evaluate the effect of the estimated trimming proportion on the a daptive estimator. We find that L-estimators with smooth weight functi ons are to be preferred to those with discontinuous weight functions ( such as the trimmed mean) because the effect of the estimated trimming proportion on the estimator is of order n(-1) rather than n(-3/4). In particular, we find that valid inferences can be based on a particula r ''smooth'' trimmed mean with its asymptotic standard error and the S tudent t distribution with degrees of freedom given by the Tukey and M cLaughlin (1963, Sankhya Ser. A, 25, 331-352) proposal.