Optimal Estimation of Parameters

This book presents a comprehensive and consistent theory of estimation. The framework described leads naturally to a generalized maximum capacity estimator. This approach allows the optimal estimation of real-valued parameters, their number and intervals, as well as providing common ground for explaining the power of these estimators. Beginning with a review of coding and the key properties of information, the author goes on to discuss the techniques of estimation and develops the generalized maximum capacity estimator, based on a new form of Shannons mutual information and channel capacity. Applications of this powerful technique in hypothesis testing and denoising are described in detail. Offering an original and thought-provoking perspective on estimation theory, Jorma Rissanens book is of interest to graduate students and researchers in the fields of information theory, probability and statistics, econometrics and finance.

Spis treści:
1. Introduction
2. Coding
3. Basics of information
4. Modeling problem
5. Other optimality properties
6. Interval estimation
7. Hypothesis testing
8. Denoising
9. Sequential models
Appendix A. Elements of algorithmic information
Appendix B. Universal prior for integers.