Variational Methods in Statistics
Published on 14. May 2014
253 pages
978-0-08-095630-5 (ISBN)
Description
Variational Methods in Statistics
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Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095630-5 (9780080956305)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Jagdish S. Rustagi
Variational Methods in Statistics
Book
01/1976
Academic Press
€66.85
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Content
- Front Cover
- Variational Methods In Statistics
- Copyright Page
- Table of Contents
- Preface
- Acknowledgements
- Chapter I. Synopsis
- 1.1 General Introduction
- 1.2 Classical Variational Methods
- 1.3 Modern Variational Methods
- 1.4 Linear Moment Problems
- 1.5 Nonlinear Moment Problems
- 1.6 Optimal Designs for Regression Experiments
- 1.7 Theory of Optimal Control
- 1.8 Miscellaneous Applications of Variational Methods in Statistics
- References
- Chapter II. Classical Variational Methods
- 2.1 Introduction
- 2.2 Variational Problem
- 2.3 Illustrations in Statistics
- 2.4 Euler-Lagrange Equations
- 2.5 Statistical Application
- 2.6 Extremals with Variable End Points
- 2.7 Extremals with Constraints
- 2.8 Inequality Derived from Variational Methods
- 2.9 Sufficiency Conditions for an Extremum
- References
- Chapter III. Modem Variational Methods
- 3.1 Introduction
- 3.2 Examples
- 3.3 Functional Equations of Dynamic Programming
- 3.4 Backward Induction
- 3.5 Maximum Principle
- 3.6 Dynamic Programming and Maximum Principle
- References
- Chapter IV. Linear Moment Problems
- 4.1 Introduction
- 4.2 Examples
- 4.3 Convexity and Function Spaces
- 4.4 Geometry of Moment Spaces
- 4.5 Minimizing and Maximizing an Expectation
- 4.6 Application of the Hahn-Banach Theorem t o Maximizing an Expectation Subject t o Constraints
- References
- Chapter V. Nonlinear Moment Problems
- 5.1 Introduction
- 5.2 Tests of Hypotheses and Neyman-Pearson Lemma
- 5.3 A Nonlinear Minimization Problem
- 5.4 Statistical Applications
- 5.5 Maximum in the Nonlinear Case
- 5.6 Efficiency of Tests
- 5.7 Type A and Type D Regions
- 5.8 Miscellaneous Applications of the Neyman-Pearson Technique
- References
- Chapter VI. Optimal Designs for Regression Experiments
- 6.1 Introduction
- 6.2 Regression Analysis
- 6.3 Optimality Criteria
- 6.4 Continuous Normalized Designs
- 6.5 Locally Optimal Designs
- 6.6 Spline Functions
- 6.7 Optimal Designs Using Splines
- Appendix to Chapter VI
- References
- Chapter VII. Theory of Optimal Control
- 7.1 Introduction
- 7.2 Deterministic Control Process
- 7.3 Controlled Markov Chains
- 7.4 Statistical Decision Theory
- 7.5 Sequential Decision Theory
- 7.6 Wiener Process
- 7.7 Stopping Problems
- 7.8 Stochastic Control Problems
- References
- Chpater VIII. Miscellaneous Applications of Variational Methods in Statistics
- 8.1 Introduction
- 8.2 Applications in Reliability
- 8.3 Bioassay Application
- 8.4 Approximations via Dynamic Programming
- 8.5 Connections between Mathematical Programming and Statistics
- 8.6 Stochastic Programming Problems
- 8.7 Dynamic Programming Model of Patient Care
- References
- Index
