Hilbert Space Methods in Probability and Statistical Inference: Small/Hilbert

Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.Content: Chapter 1 Introduction (pages 1–8): Chapter 2 Hilbert Spaces (pages 9–30): Chapter 3 Probability Theory (pages 31–57): Chapter 4 Estimating Functions (pages 59–105): Chapter 5 Orthogonality and Nuisance Parameters (pages 107–125): Chapter 6 Martingale Estimating Functions and Projected Likelihood (pages 127–161): Chapter 7 Stochastic Integration and Product Integrals (pages 163–187): Chapter 8 Estimating Functions and the Product Integral Likelihood for Continuous Time Stochastic Processes (pages 189–220): Chapter 9 Hilbert Spaces and Spline Density Estimation (pages 221–234): 1. Introduction -- 2. Hilbert Spaces -- 3. Probability Theory -- 4. Estimating Functions -- 5. Orthogonality And Nuisance Parameters -- 6. Martingale Estimating Functions And Projected Likelihood -- 7. Stochastic Integration And Product Integrals -- 8. Estimating Functions And The Product Integral Likelihood For Continuous Time Stochastic Processes -- 9. Hilbert Spaces And Spline Density Estimation. Christopher G. Small, D.l. Mcleish. A Wiley-interscience Publication. Includes Bibliographical References (p. 235-244) And Index.