Abstract
This chapter is introductory. It discusses the general question of selecting a model for a problem of statistical inference, and motivates the choice of the assumption of stationarity. This and other related models considered in the literature are discussed and compared. Furthermore, a general and informal overview of the results presented in the book is given, highlighting the interplay between impossibility and consistency results.
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Notes
- 1.
Here we are only concerned with separable metric spaces.
- 2.
To make complete sense of this sentence, we would need to define the distances formally first, which is done in the next chapter. We shall see that the definition of the distributional distance is ambiguous: it depends on a set of parameters, changing which may change the resulting topology. However, it is possible to make this statement formally correct.
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Ryabko, D. (2019). Introduction. In: Asymptotic Nonparametric Statistical Analysis of Stationary Time Series. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-12564-6_1
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