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Abstract
We propose a robust testing procedure, namely the smooth adaptive test (SA test) for testing the population mean. The SA test is constructed by using the smooth adaptive (SA) estimator (Han and Hawkins, 1994, Communication in Statistics-Theory and Methods, 23, 1-10). In the one-sample problem of testing the mean equal to a specified value, we investigate the probability of Type I error and the power of the proposed SA test via a Monte Carlo simulation. The SA test is compared with other tests such as normal test, t test and signed-rank test. In the two-sample problem of testing the equality of two means, we use the difference of the smooth adaptive estimators to estimate the difference of the two population means. We also study the probability of Type I error and the power of the SA test and compare it with the t test, Behrens-Fisher approximation t test and Wilcoxon and Mann-Whitney test. The bootstrap technique is used to construct confidence intervals for means in both cases. The SA test is investigated under the situations of with and without outliers.
