Abstract
In this introductory chapter, we first recall some basic concepts from mathematical statistics regarding statistical decision theory and, in particular, statistical test theory. Then, we deal with the concepts of conditional distributions and conditional expectations in a general manner. The treatment is based on a construction by means of Markov kernels. Finally, we give an introduction to the theory of nonparametric tests, and we discuss the specific examples of bootstrap tests (for one-sample problems) and permutation tests (for multi-sample problems) on a conceptual level.
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Notes
- 1.
Witting (1985): “We think of all the data material summarized as one “observation” […].” (translation by the author, the observation will be denoted as Y = y).
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Dickhaus, T. (2018). Introduction and Examples. In: Theory of Nonparametric Tests. Springer, Cham. https://doi.org/10.1007/978-3-319-76315-6_1
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