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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.

Statistical science --- Topology --- Mathematical analysis --- Mathematics --- Mathematical physics --- Applied physical engineering --- analyse (wiskunde) --- toegepaste wiskunde --- economie --- statistiek --- wiskunde --- fysica --- topologie --- statistisch onderzoek --- Mathematical statistics. --- Mathematics. --- Global analysis (Mathematics). --- Topology. --- Statistical Theory and Methods. --- Applications of Mathematics. --- Analysis. --- Mathematical Physics. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Engineering --- Engineering analysis --- Statistical analysis --- Statistical data --- Econometrics --- R (Computer program language). --- GNU-S (Computer program language) --- Domain-specific programming languages

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Infinite-dimensional manifolds. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Manifolds, Infinite-dimensional --- Topological manifolds

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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.

Statistical science --- Topology --- Mathematical analysis --- Mathematics --- Mathematical physics --- Applied physical engineering --- analyse (wiskunde) --- toegepaste wiskunde --- economie --- statistiek --- wiskunde --- fysica --- topologie --- statistisch onderzoek