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Functional Approach to Optimal Experimental Design

  • Book
  • © 2006

Overview

Authors:
  1. Viatcheslav B. Melas

    1. Mathematics & Mechanics Faculty, St. Petersburg State University, St. Petersburg, Russia

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  • Consiers optimal designs for a wide class of models
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Statistics (LNS, volume 184)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    Pages 1-4

  3. Fundamentals of the Optimal Experimental Design

    Pages 5-21

  4. The Functional Approach

    Pages 23-70

  5. Polynomial Models

    Pages 71-133

  6. Trigonometrical Models

    Pages 135-195

  7. D-Optimal Designs for Rational Models

    Pages 197-216

  8. D-Optimal Designs for Exponential Models

    Pages 217-230

  9. E- and c-Optimal Designs

    Pages 231-271

  10. The Monod Model

    Pages 273-316

  11. Back Matter

    Pages 317-333
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Keywords

About this book

The present book is devoted to studying optimal experimental designs for a wide class of linear and nonlinear regression models. This class includes polynomial, trigonometrical, rational, and exponential models as well as many particular models used in ecology and microbiology. As the criteria of optimality, the well known D-, E-, and c-criteria are implemented. The main idea of the book is to study the dependence of optimal - signs on values of unknown parameters and on the bounds of the design interval. Such a study can be performed on the base of the Implicit Fu- tion Theorem, the classical result of functional analysis. The idea was ?rst introduced in the author’s paper (Melas, 1978) for nonlinear in parameters exponential models. Recently, it was developed for other models in a n- ber of works (Melas (1995, 2000, 2001, 2004, 2005), Dette, Melas (2002, 2003), Dette, Melas, Pepelyshev (2002, 2003, 2004b), and Dette, Melas, Biederman (2002)). Thepurposeofthepresentbookistobringtogethertheresultsobtained and to develop further underlying concepts and tools. The approach, m- tioned above, will be called the functional approach. Its brief description can be found in the Introduction. The book contains eight chapters. The ?rst chapter introduces basic concepts and results of optimal design theory, initiated mainly by J.Kiefer.

Reviews

From the reviews:

"This monograph is a welcome addition to the statistical literature on optimal experimental designs. … This will be a useful reference book for researchers in this area." (Damaraju Raghavarao, Mathematical Reviews, Issue 2006 k)

"The material presented is at a sophisticated mathematical level, with a strong emphasis on the construction to why these strategies create designs that are desirable for practical implementation. The unified approach helps consolidate the individual pieces that the author has published previously, and provides greater insights into the applicability of the methods." (Christine M. Anderson-Cook, Journal of the American Statistical Association, Vol. 102, No. 477, 2007)

Authors and Affiliations

  • Mathematics & Mechanics Faculty, St. Petersburg State University, St. Petersburg, Russia

    Viatcheslav B. Melas

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