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.

Hilbert Spaces. Probability Theory. Estimating Functions. Orthogonality and Nuisance Parameters. Martingale Estimating Functions and Projected Likelihood. Stochastic Integration and Product Integrals. Estimating Functions and the Product Integral Likelihood forContinuous Time Stochastic Processes. Hilbert Spaces and Spline Density Estimation. Bibliography. Index.