Ebook: Hilbert Space Methods in Probability and Statistical Inference

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):