TY  - BOOK
AU  - Pantsulaia,Gogi
ED  - SpringerLink (Online service)
TI  - Applications of Measure Theory to Statistics
SN  - 9783319455785
AV  - QA276-280 
U1  - 519.5 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematical statistics
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Topology
KW  - Statistical Theory and Methods
KW  - Applications of Mathematics
KW  - Analysis
KW  - Mathematical Physics
N1  - 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?
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-45578-5
ER  -