In 1945 Wilcoxon proposed a nonparametric statistical hypothesis test for the case of two related samples or repeated measurements on a single sample. The Wilcoxon signed rank test is distribution-free in the sense that its use does not require assumptions about the form of the distribution of measurements. It can be used for testing the hypothesis of symmetry. In 2008 Stute introduced a large class of weighted U-statistics of order statistics that, with a specific choice of weight and kernel functions, lead to weighted Wilcoxon-type tests for symmetry. A class of weighted Wilcoxon-type tests includes the classical Wilcoxon test as a particular case. In this thesis, efficiency properties of weighted Wilcoxon-type tests for large sample sizes are investigated. The Pitman efficiency of weighted Wilcoxon-type tests is calculated. Some illustrative examples are included. The main results of the thesis are new.
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