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Foundations of Estimation Theory
The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapters on linear and quadratic estimations, and normality of observation vectors have been included. Chapter 2 inclu...
Lessons in Estimation Theory for Signal Processing, Communications, and Control
Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering. To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are interrelated. Written as a collection of lessons, this book introduces readers o the general field of estimation theory and includes abundant supplementary material.
Parameter Estimation
Introduction and historical perspective; Least-squares estimation; General characteristics of estimators; Mean-square and minimum variance estimators; Maximum a posteriori and maximum likelihood estimators; Numerical solution of least-squares and maximum likelihood estimation problems; Sequential estimators and some asymptotic properties.
Theory of Point Estimation
This book is concerned with point estimation in Euclidean sample spaces. The first four chapters deal with exact (small-sample) theory, and their approach and organization parallel those of the companion volume, Testing Statistical Hypotheses (TSH). Optimal estimators are derived accord ing to criteria such as unbiasedness, equivariance, and minimaxity, and the material is organized around these criteria. The principal applications are to exponential and group families, and the systematic discussion of the rich body of (relatively simple) statistical problems that fall under these headings constitutes a second major theme of the book. A theory of much wider applicability is obtained by adopt...
STATISTICAL INFERENCE : THEORY OF ESTIMATION
This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimat...
Theory of Preliminary Test and Stein-Type Estimation with Applications
Theory of Preliminary Test and Stein-Type Estimation withApplications provides a com-prehensive account of the theory andmethods of estimation in a variety of standard models used inapplied statistical inference. It is an in-depth introduction tothe estimation theory for graduate students, practitioners, andresearchers in various fields, such as statistics, engineering,social sciences, and medical sciences. Coverage of the material isdesigned as a first step in improving the estimates before applyingfull Bayesian methodology, while problems at the end of eachchapter enlarge the scope of the applications. This book contains clear and detailed coverage of basic terminologyrelated to various topics, including: * Simple linear model; ANOVA; parallelism model; multipleregression model with non-stochastic and stochastic constraints;regression with autocorrelated errors; ridge regression; andmultivariate and discrete data models * Normal, non-normal, and nonparametric theory of estimation * Bayes and empirical Bayes methods * R-estimation and U-statistics * Confidence set estimation
Multivariate Density Estimation
Written to convey an intuitive feel for both theory and practice, its main objective is to illustrate what a powerful tool density estimation can be when used not only with univariate and bivariate data but also in the higher dimensions of trivariate and quadrivariate information. Major concepts are presented in the context of a histogram in order to simplify the treatment of advanced estimators. Features 12 four-color plates, numerous graphic illustrations as well as a multitude of problems and solutions.
