Overview
- Helps the reader to understand some conjectures arising in the criticism of null hypothesis significance testing (NHST)
- Includes a special chapter that helps the reader to calculate infinite-dimensional Riemann integrals over infinite-dimensional rectangles in R8
- Considers how to construct objective consistent estimates of an unknown parameter in a Polish group
- Includes supplementary material: sn.pub/extras
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Gogi Rauli Pantsulaia graduated with a degree in Mathematics from the Iv. Javakhishvili Tbilisi State University (Georgia) in 1982, and received his Ph.D. in Mathematics from the Institute of Mathematics of the Ukrainian Academy of Sciences in 1985. In 2003 he completed his degree of doctor of physics and mathematics at the I. Vekua Institute of Applied Mathematics of the Iv. Javakhishvili Tbilisi State University (Georgia). He is currently a professor at the Department of Mathematics of the Georgian Technical University. He has participated in more than 10 major research projects and is the author of 4 books and more than 75 papers. His current research interests include set theory, measure theory, probability theory and mathematical statistics.
Bibliographic Information
Book Title: Applications of Measure Theory to Statistics
Authors: Gogi Pantsulaia
DOI: https://doi.org/10.1007/978-3-319-45578-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-45577-8Published: 04 January 2017
Softcover ISBN: 978-3-319-83322-4Published: 29 April 2018
eBook ISBN: 978-3-319-45578-5Published: 22 December 2016
Edition Number: 1
Number of Pages: XV, 134
Topics: Statistical Theory and Methods, Applications of Mathematics, Analysis, Mathematical Physics, Topology