A Biweight Approach to the One-Sample Problem

Abstract

A “ t ”-like statistic, replacing the classical mean by a biweight location estimator in the numerator and the sample variance by a corresponding variance term in the denominator, is proposed as a modification to that used by Gross (1976) and is evaluated for its efficiency in constructing confidence intervals in symmetric, stretched-tailed situations. The one-sample biweight “ t ” is shown, via Monte Carlo simulations, to be efficient for samples of moderate sizes (in terms of expected length of the confidence intervals). For smaller samples (size five), the sum of the biweight weights is useful in rescaling biweight “ t ”. For several samples of common population width, a root mean square of the variances affords greater stability when the underlying distribution is not extremely stretched-tailed.