Abstract
Under the assumption of differentiability in the mean, we discuss parametric score tests. In the case of one-sided test problems with one-dimensional parameter spaces, score tests are locally optimal. Based on this motivation, we derive rank tests for two-sample problems, by means of conditioning on the ranks of the observables and calculating the corresponding score function. This leads to classical nonparametric tests like Wilcoxon’s rank sum test or the log-rank test. Finally, we provide an alternative justification of two-sample rank tests, which is based on statistical functionals.
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Dickhaus, T. (2018). Rank Tests. In: Theory of Nonparametric Tests. Springer, Cham. https://doi.org/10.1007/978-3-319-76315-6_4
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DOI: https://doi.org/10.1007/978-3-319-76315-6_4
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