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Optimization techniques in statistics /
Statistics help guide us to optimal decisions under uncertainty. A large variety of statistical problems are essentially solutions to optimization problems. The mathematical techniques of optimization are fundamentalto statistical theory and practice. In this book, Jagdish Rustagi provides full-spec...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston :
Academic Press,
�1994.
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| Colección: | Statistical modeling and decision science.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Optimization Techniques in Statistics; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter 1. Synopsis; 1.1 Introduction; 1.2 Classical Optimization Techniques; 1.3 Optimization and Inequalities; 1.4 Numerical Methods of Optimization; 1.5 Linear Programming Techniques; 1.6 Nonlinear Programming Techniques; 1.7 Dynamic Programming Methods; 1.8 Variational Methods; 1.9 Stochastic Approximation Procedures; 1.10 Optimization in Simulation; 1.11 Optimization in Function Spaces; Chapter 2. Classical Optimization Techniques; 2.1 Introduction; 2.2 Preliminaries
- 2.3 Necessary and Sufficient Conditions for an Extremum2.4 Constrained Optimization-Lagrange Multipliers; 2.5 Statistical Applications; 2.6 Exercises; Chapter 3. Optimization and Inequalities; 3.1 Introduction; 3.2 Classical Inequalities; 3.3 Matrix Inequalities; 3.4 Applications; Chapter 4. Numerical Methods of Optimization; 4.1 Introduction; 4.2 Numerical Evaluation of Roots of Equations; 4.3 Direct Search Methods; 4.4 Gradient Methods; 4.5 Convergence of Numerical Procedures; 4.6 Nonlinear Regression and Other Statistical Algorithms; 4.7 Exercises; Chapter 5. Linear Programming Techniques
- 5.1 Introduction5.2 Linear Programming Problem; 5.3 Standard Form of the Linear Programming Problem; 5.4 Simplex Method; 5.5 Karmarkar's Algorithm; 5.6 Zero-Sum Two-Person Finite Games and Linear Programming; 5.7 Integer Programming; 5.8 Statistical Applications; 5.9 Exercises; Chapter 6. Nonlinear Programming Methods; 6.1 Introduction; 6.2 Statistical Examples; 6.3 Kuhn-Tucker Conditions; 6.4 Quadratic Programming; 6.5 Convex Programming; 6.6 Applications; 6.7 Statistical Control of Optimization; 6.8 Stochastic Programming; 6.9 Geometric Programming; 6.10 Exercises
- Chapter 7. Dynamic Programming Methods7.1 Introduction; 7.2 Regulation and Control; 7.3 Functional Equation and Principles of Optimality; 7.4 Dynamic Programming and Approximation; 7.5 Patient Care through Dynamic Programming; 7.6 Pontryagin Maximum Principle; 7.7 Miscellaneous Applications; 7.8 Exercises; Chapter 8. Variational Methods; 8.1 Introduction; 8.2 Statistical Applications; 8.3 Euler-Lagrange Equations; 8.4 Neyman-Pearson Technique; 8.5 Robust Statistics and Variational Methods; 8.6 Penalized Maximum Likelihood Estimates; 8.7 Exercises
- Chapter 9. Stochastic Approximation Procedures9.1 Introduction; 9.2 Robbins-Monro Procedure; 9.3 General Case; 9.4 Kiefer-Wolfowitz Procedure; 9.5 Applications; 9.6 Stochastic Approximation and Filtering; 9.7 Exercises; Chapter 10. Optimization in Simulation; 10.1 Introduction; 10.2 Optimization Criteria; 10.3 Optimality of Regression Experiments; 10.4 Response Surface Methods; 10.5 Miscellaneous Stochastic Methods; 10.6 Application; Chapter 11. Optimization in Function Spaces; 11.1 Introduction; 11.2 Preliminaries; 11.3 Optimization Results; 11.4 Splines in Statistics; 11.5 Exercises