On the combination of the sign and Maesono tests for simmetry and its efficiency

Abstract

We propose a new test for the simmetry hypothesis which is a combination of the sign statistic and the Wr Maesono statistic. The latter generalizes the Wilcoxon statistic and coincides with it for r = 2. The proposed statistic belongs to the class of non-degenerate U-statistics and hence it has asymptotically normal distribution. We calculate its Pitman efficacy and compare it with the t-test. For instance, in the normal case, for r=4, the new test, with respect t t-test, has a higher efficiency (0,9794) than the Wilcoxon test (0,9549). In the logistic case, G4 has a higher efficincy (1,0939) than the t-test.