Rissanen J. Optimal Estimation of Parameters

Cambridge: Cambridge University Press, 2012. — 171 p.This book presents a comprehensive and consistent theory of estimation. The framework described leads naturally to the maximum capacity estimator as a generalization of the maximum likelihood 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 Shannon’s 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 Rissanen’s book is of interest to graduate students and researchers in the fields of information theory, probability and statistics, econometrics, and finance.