ON ASYMPTOTICALLY ROBUST COMPETITORS OF THE ONE-SAMPLE T-TEST.
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
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Although the t-test is one of the most commonly used statistical procedures, its behavior is somewhat sensitive to the assumption that the observations come from a normal distribution. Recently, it has been shown that quick estimators, i.e., estimators which are linear combinations of a few sample quantiles are robust estimators of the location parameter for a large class of symmetric unimodal densities. In order to use the median or any other quick estimator as a test we must estimate its variance, or in large samples its asymptotic variance. The present paper is concerned with estimating 1f squared nu subscript p where nu subscript p is the true value of the p-th population quantile and fx is the density function. The estimator we consider has properties similar to those of Rosenblatts estimate of a density function.
- Statistics and Probability