Stochastic Processes - Inference Theory

This is the revised and enlarged 2nd edition of the authors' original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics.

The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.

1. Introduction and Preliminaries. - 2. Some Principles of Hypothesis Testing. - 3. Parameter Estimation and Asymptotics. - 4. Inferences for Classes of Processes. - 5. Likelihood Ratios for Processes. - 6. Sampling Methods for Processes. - 7. More on Stochastic Inference. - 8. Prediction and Filtering of Processes. - 9. Nonparametric Estimation for Processes. - Bibliography. - Index.