Optimization Techniques in Statistics

Optimization Techniques in Statistics

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Description

The mathematical techniques of optimization are fundamental to statistical theory and practice. This volume covers these methods, ranging from classical optimization and Lagrange multipliers, to numerical techniques using gradients or direct search, to linear, nonlinear and dynamic programming using the Kuhn-Tucker conditions or the Pontryagin maximal principle. Variational methods and optimization in function spaces are also discussed, as are stochastic optimization in simulation, including annealing methods. The text features various applications, including: estimates of maximum likelihood; Markov decision processes; programming methods used to optimize monitoring of patients in hospitals; the derivation of the Neyman-pearson lemma; the search for optimal designs; and the simulation of a steel mill.
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Product details

  • Hardback | 352 pages
  • 152 x 226 x 22mm | 680.4g
  • Academic Press Inc
  • San Diego, United States
  • English
  • bibliography, index
  • 0126045550
  • 9780126045550

Table of contents

Synopsis: Classical Optimisation Techniques, Optimisation and Inequalities, Numerical Methods of Optimisation, Linear Programming Techniques, Non-linear Programming Techniques, Dynamic Programming Methods, Variational Methods, Stochastic Approximation Procedures, Optimisation in Simulation, Optimisation in Function Spaces; Classical Optimisation Techniques: Preliminaries, Necessary and Sufficient Conditions for an Extremum, Constrained Optimisation - Lagrange Multipliers, Statistical Applications; Optimisation and Inequalities: Classical Inequalities, Matrix Inequalities, Applications; Numerical Methods of Optimisation: Numerical Evaluation of Roots of Equations, Direct Search Methods, Gradient Methods, Convergence of Numerical Procedures, Non-linear Regression and Other Statistical Algorithms; Linear Programming Techniques: Linear Programming Problem, Standard Form of the Linear Programming Problem, Simplex Method, Karmarkar's Algorithm, Zero-Sum Two Person Finite-Games and Linear Programming, Integer Programming, Statistical Applications; Non-linear Programming Methods: Statistical Examples, Kuhn-Tucker Conditions, Quadratic Programming, Convex Programming, Applications, Statistical Control of Optimisation, Stochastic Programming, Geometric Programming; Dynamic Programming Methods: Regulation and Control, Functional Equation and Principles of Optimality, Dynamic Programming and Approximation, Patent Care through Dynamic Programming, Pontryagin Maximum Principle, Miscellaneous Applications; Variational Methods: Statistical Applications, Euler-Lagrange Equations, Neyman-Pearson Technique, Robust Statistics and Variational Methods, Penalised Maximum Likelihood Estimates; Stochastic Approximation Procedures: Robbins-Monro Procedure, General Case, Kiefer-Wolfowitz Procedure, Applications, Stochastic Approximation and Filtering; Optimisation in Simulation: Optimisation Criteria, Optimality of Regression Experiments, Response Surface Methods, Miscellaneous Stochastic Methods, Application; Optimisation in Function Spaces: Preliminaries, Optimisation Results, Splines in Statistics, Chapter Exercises, Bibliography; Index.
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Review quote

It is well written, nicely organized, with a high degree of mathematical accuracy...all coming together to make the material easily digestible.--Stergios B. Fotopoulos, Washington State University
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