Optimization Techniques in Statistics
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Abstract
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.