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Applications of Measure Theory to Statistics
ISBN-13:
9783319455785
Veröffentl:
2016
Seiten:
134
Autor:
Gogi Pantsulaia
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
1 Calculation of Improper Integrals by Using Uniformly Distributed Sequences.- 2 Infinite-Dimensional Monte-Carlo Integration.- 3 On structure of all real-valued sequences uniformly distributed in [-1/2;1/2] from the point of view of shyness.- 4 On Moore-Yamasaki-Kharazishvili type measures and the infinite powers of Borel diffused probability measures on R.- 5 On objective and strong objective consistent estimates of unknown parameters for statistical structures in a Polish group admitting an invariant metric.- 6 Why Null Hypothesis is rejected for "almost every" infinite sample by the Hypothesis Testing of a maximal reliability?.
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