Comparison of Statistical Experiments

Erscheinungsjahr 2008
ISBN: 978-0-521-10282-7
Verlag: Cambridge University Press

Buch, Englisch, Band 36, 696 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1039 g

Reihe: Encyclopedia of Mathematics and its Applications

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

Autoren/Hrsg.

Torgersen, Erik

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Entscheidungstheorie, Sozialwahltheorie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Preface; Acknowledgements; 1. Statistical experiments within the measure theoretical framework; 2. Convexity; 3. Two-person, zero-sum games; 4. Statistical decision problems; 5. Vector lattices; 6. Deficiencies; 7. Equivalence, representations and functionals of experiments; 8. Comparison of linear models; 9. Majorisation and approximate majorisation; 10. Complements: Further examples, problems and comments; List of symbols; Author index; Additional references; Subject index.