ENGLISH

Applications of Measure Theory to Statistics

By Gogi Pantsulaia

Book information

Publisher
SPRINGER INTERNATIONAL PU
Year
2016
ISBN
331945577X, 978-3-319-45577-8, 978-3-319-45578-5, 3319455788
Language
english
Format
PDF
Filesize
1 MB (1097868 bytes)
Edition
1st ed.
Pages
134\147
Library
kolxoz
Time added
2017-10-15 16:00:00

Description

This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics. Front Matter....Pages i-xv Calculation of Improper Integrals by Using Uniformly Distributed Sequences....Pages 1-18 Infinite-Dimensional Monte Carlo Integration....Pages 19-46 Structure of All Real-Valued Sequences Uniformly Distributed in \([-\frac{1}{2}, \frac{1}{2}]\) from the Point of View of Shyness....Pages 47-56 On Moore–Yamasaki–Kharazishvili Type Measures and the Infinite Powers of Borel Diffused Probability Measures on R....Pages 57-71 Objective and Strong Objective Consistent Estimates of Unknown Parameters for Statistical Structures in a Polish Group Admitting an Invariant Metric....Pages 73-106 Why Null Hypothesis Is Rejected for Almost Every Infinite Sample by the Hypothesis Testing of a Maximal Reliability....Pages 107-118 Back Matter....Pages 119-134

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