Variational Methods in Statistics

Name: Variational Methods in Statistics
Brand: Academic Press
Price: 71.95 EUR
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Rustagi(Autor*in)

Rustagi(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

253 Seiten

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Inhalt

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

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