Parameter Estimation for Scientists and Engineers

ISBN-13: 9780470147818 / Angielski / Twarda / 2007 / 288 str.

Adriaan Van Den Bos

Opis

The subject of this book is estimating parameters of expectation models of statistical observations. The book describes the most important aspects of the subject for applied scientists and engineers. This group of users is often not aware of estimators other than least squares. Therefore one purpose of this book is to show that statistical parameter estimation has much more to offer than least squares estimation alone. In the approach of this book, knowledge of the distribution of the observations is involved in the choice of estimators. A further advantage of the chosen approach is that it unifies the underlying theory and reduces it to a relatively small collection of coherent, generally applicable principles and notions.

Recenzje

An indispensable tool for scholars and research workers in mathematics and the mathematical sciences. ( Mathematical Reviews, 2009)

"Despite its lean size, the book is able to cover many of the techniques and theories in parameter estimation that are core to applied sciences, and so this is certainly a valuable reference for researchers and graduate students alike. The book′s exposition is lucid, making it an accessible reading for someone with a reasonable background in elementary statistics. Thus I think anyone in applied sciences and engineering dealing with the implementation of expectation models and aiming to estimate model parameters will find this book helpful. This is a great addition to resources in learning or reviewing statistical tools that emphasize taking advantage of valuable information from data and improving the precision of estimation." (Technometrics, November 2008)

"I highly recommend this book to practitioners who want to systematically learn and use, new, better techniques for parameter estimation." (Computing Reviews, September 10, 2008)

" appropriate for students in advanced applied statistics courses even more useful as a supplemental resource " (CHOICE, January 2008)

Spis treści

Preface.

1 Introduction.

2 Parametric Models of Observations.

3 Distributions of Observations.

4 Precision and Accuracy.

5 Precise and Accurate Estimation.

6 Numerical Methods for Parameter Estimation.

7 Solutions or Partial Solutions to Problems.

Appendix A: Statistical Results.

Appendix B: Vectors and Matrices.

Appendix C: Positive Semidefinite and Positive Definite Matrices.

Appendix D: Vector and Matrix Differentiation.

References.

Topic Index.

O autorze

Adriaan van den Bos, PhD, is Professor Emeritus of the Department of Applied Physics of Delft University of Technology, The Netherlands. He carries out research in the field of statistical signal processing, parameter estimation, statistics, and application of parameter estimation to problems in applied physics, to optics and electron–optics in particular. He authored or coauthored some fifty journal papers, and his paper "Alternative Interpretation of Maximum Entropy Spectral Analysis," published in IEEE Transactions on Information Theory in 1971, became an official Citation Classic. In addition to journal papers, he has contributed to a number of books. In 2000, Dr. van den Bos was elected to the grade of Fellow of the Institute of Electrical and Electronics Engineers for his fundamental work in modeling and identification and its application in instrumentation and signal processing.

Blurb

Step–by–Step Methodology for Practical Parameter Estimation

Written for applied scientists and engineers, this book covers the most important aspects of estimating parameters of expectation models of statistical observations. The author demonstrates that statistical parameter estimation has much more to offer than least squares estimation alone, and explains how a priori knowledge may be used more fully to improve the precision of estimating. Parameter Estimation for Scientists and Engineers presents:

• An explanation of statistical parametric models of observations, and why they are used

• A description of distributions of observations including exponential families of distributions

• Fisher information and the Cramér–Rao lower bound, and how they are used to judge the quality of parameter estimators and experimental designs

• The maximum likelihood method and the least squares method for estimating parameters of expectation models

• A discussion of model hypothesis testing

• Numerical methods suitable for the parameter estimation problems dealt with in this book, as well as an exploration of how to use these methods in practice

Complete with sixty–two examples, eighty–nine problems and solutions, and thirty–four figures, Parameter Estimation for Scientists and Engineers is an invaluable reference for professionals and an ideal text for advanced undergraduate and graduate–level students in all disciplines of engineering and applied science.