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Mathematical basis of statistics

Author: Jean René Barra; Z W Birnbaum; E Lukacs
Publisher: Burlington : Academic Press/Elsevier Science, [2014], ©1981.
Series: Probability and mathematical statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Mathematical Basis of Statistics.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Barra, Jean-René.
Mathematical Basis of Statistics : Probability and Mathematical Statistics: A Series of Monographs and Textbooks.
Burlington : Elsevier Science, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean René Barra; Z W Birnbaum; E Lukacs
ISBN: 9781483191447 1483191443
OCLC Number: 898771873
Notes: CHAPTER 11. Testing Hypotheses on Exponential Statistical Spaces.
Description: 1 online resource (269 pages).
Contents: 5.P-Minimum Sufficient Subfields and Statistics6. Relationship among Freedom, Completeness, Sufficiency, and StochasticIndependence; 7. Existence of Free Events; Exercises; CHAPTER 3. Statistical Information; 1. Introduction; 2. Information (according to Fisher); Exercises; CHAPTER 4. Statistical Inference; 1. Introduction; 2. Decisions and Strategies; 3. Hypothesis Testing and Statistical Estimation; 4. Choosing a Strategy; 5. Quasi-Ordering Induced by a Loss Function; 6. Nuisance Parameters; Exercises; CHAPTER 5. Testing Statistical Hypotheses; 1. Definitions and Preliminary Remarks. 2. Quasi-Ordering on Tests of Hypotheses3. Optimal Tests; 4. The Fundamental Neyman-Pearson Lemma; 5. Determining Optimal Tests; 6. Nonoptimal Methods; Exercises; CHAPTER 6. Statistical Estimation; 1. Unbiased Estimators; 2. Optimal Estimators; 3. Construction of Confidence Regions; 4. Optimal Set Estimators; Exercises; CHAPTER 7. The Multivariate Normal Distribution; 1. Some Useful Distributions; 2. Multivariate Normal Distributions; 3. Quadratic Forms of Normal Vectors; 4. Stochastic Dependence among Normal Vectors; Exercises; CHAPTER 8. Random Matrices; 1. Notation. 2. Covariance and Characteristic Function of a Random Matrix3. Some Miscellaneous Results; 4. Fundamental Results; 5. Normal Random Matrix; 6. Generalized Gamma Distributions; 7. Bartlett's Decomposition of a Gamma Distribution; 8. Nonsingular Gamma Distribution; 9. Generalized Beta Distributions; 10. Generalized Noncentral Gamma Distributions; Exercises; CHAPTER 9. Linear-Normal Statistical Spaces; 1. The Cochran Theorem; 2. Linear-Normal Statistical Spaces; 3. Fundamental Theorems; 4. Testing Linear Hypotheses; 5. Estimation of Linear Functions. 6. Fundamental Lemmas for Analysis of Variance7. Methodology of Analysis of Variance (Model I) in Experimental Design; 8. Analysis of Variance for Some Standard Experimental Designs; 9. Introduction to Analysis of Variance (Model II); 10. Generalized Linear-Normal Statistical Spaces; Exercises; CHAPTER 10. Exponential Statistical Spaces; 1. Laplace Transform of a Measure; 2. Analytical Properties of Exponential Statistical Spaces; 3. Sufficient Statistics on an Exponential Statistical Space; 4. Incomplete Exponential Statistical Spaces; 5. The Behrens-Fisher Problem; Exercises.
Series Title: Probability and mathematical statistics.
Other Titles: Notions fondamentales de statistique mathématique.
Responsibility: Jean-René Barra ; translation edited by Leon Herbach.

Abstract:

Mathematical Basis of Statistics.

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