Abstract: The aim of this thesis was to introduce the concept of U-statistics as unbiased estimators
of statistical expectation functionals. Special emphasis was put on the application and
properties of U-statistics. Further in the thesis, several examples of U-statistics which are
used in the assessment of parameters that can be represented by using expectation functionals
were given. Additionally, important theorems regarding variance, asymptotic variance as
well as asymptotic normality of U-statistics have been proven. In order to demonstrate
the application of the u-statistics, Wilcoxon signed rank test was explained in detail, both
theoretically and by example. Since asymptotic distribution of Wilcoxon signed rank teststatistics
corresponds to the asymptotic distribution of a specific U-statistics, properties of
U-statistics were used to show asymptotic normality of Wilcoxon signed rank test-statistics.
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: dissertation
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