Applications of Measure Theory to Statistics - Hardcover

Pantsulaia, Gogi

Hardcover

ISBN 10: 331945577X ISBN 13: 9783319455778

Verlag: Springer, 2017

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2017
• Sprache: Englisch
• ISBN 10: 331945577X
• ISBN 13: 9783319455778
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 149
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland