TY - GEN digital ID - 131565560 TI - Applications of Measure Theory to Statistics PY - 2016 SN - 9783319455785 PB - Cham Springer International Publishing DB - UniCat KW - Statistical science KW - Topology KW - Mathematical analysis KW - Mathematics KW - Mathematical physics KW - Applied physical engineering KW - analyse (wiskunde) KW - toegepaste wiskunde KW - economie KW - statistiek KW - wiskunde KW - fysica KW - topologie KW - statistisch onderzoek UR - https://www.unicat.be/uniCat?func=search&query=sysid:131565560 AB - 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. ER -