2016 | Buch
Applications of Measure Theory to Statistics
Autor: Gogi Pantsulaia
Verlag: Springer International Publishing
Print ISBN: 978-3-319-45577-8
Electronic ISBN: 978-3-319-45578-5
2016 | Buch
Autor: Gogi Pantsulaia
Verlag: Springer International Publishing
Print ISBN: 978-3-319-45577-8
Electronic ISBN: 978-3-319-45578-5
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.