Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization 1

Abstract

The vulnerability of Student's t, insofar as efficiency and power are concerned, leads to consideration of substitutes. Among the most promising are ratios of trimmed means to square roots of suitable quadratic forms involving the same order statistics. Matching, across underlying distributions, of ratios of average of denominator to variance of numerator leads to selection of the Winsorized sum of squared deviations as the basis for a denominator. The resulting trimmed t should prove more useful when the amount of trimming is made to depend on the individual sample in a suitably prescribed manner. Exact critical values for the resulting tailored t seem to require Monte Carlo computation, but use of a simple modified denominator for trimmed t allows us to use the conventional t tables as a reasonable approximation.