Why Null Hypothesis Is Rejected for Almost Every Infinite Sample by the Hypothesis Testing of a Maximal Reliability

Gogi Pantsulaia ()
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Gogi Pantsulaia: Georgian Technical University, Department of Mathematics

Chapter Chapter 6 in Applications of Measure Theory to Statistics, 2016, pp 107-118 from Springer

Abstract: Abstract The notion of Haar null sets was introduced by J. P. R. Christensen in 1973 and reintroduced in 1992 in the context of dynamical systems by Hunt, Sauer, and Yorke. During the last 20 years this notion has been useful in studying exceptional sets in diverse areas. These include analysis, dynamical systems, group theory, and descriptive set theory. In the present chapter their notion of “prevalence” is used in studying structures of domains of some infinite sample statistics and in explaining why null hypothesis is rejected for almost every infinite sample by the hypothesis testing of a maximal reliability.

Keywords: Null Hypothesis; Statistical Decision; Topological Vector Space; Consistent Estimator; Borel Probability Measure (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-45578-5_6

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