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1. 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 -- 2. Classical Variational Methods; 2.1 Introduction; 2.2 Variational Problem; 2.3 Illustrations in Statistics; 2.4 Euler-Lagrange Equations; 2.5 Statistical Application2.6 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 -- 3. 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 -- 4. 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 Expectation4.6 Application of the Hahn-Banach Theorem to Maximizing an Expectation Subject to Constraints; References -- 5. 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 -- 6. Optimal Designs for Regression Experiments; 6.1 Introduction; 6.2 Regression Analysis. 6.3 Optimality Criteria6.4 Continuous Normalized Designs; 6.5 Locally Optimal Designs; 6.6 Spline Functions; 6.7 Optimal Designs Using Splines; Appendix to Chapter VI; References -- 7. 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 -- 8. Miscellaneous Applications of Variational Methods in Statistics; 8.1 Introduction; 8.2 Applications in Reliability
8.3 Bioassay Application8.4 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 -- Description
Variational methods in statistics.