Functional Approach to Optimal Experimental Design

ISBN-13: 9780387987415 / Angielski / Miękka / 2005 / 338 str.

Viatcheslav B. Melas; V. B. Melas

Opis

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.

Recenzje

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)

Spis treści

Fundamentals of the Optimal Experimental Design.- The Functional Approach.- Polynomial Models.- Trigonometrical Models.- D-Optimal Designs for Rational Models.- D-Optimal Designs for Exponential Models.- E- and c-Optimal Designs.- The Monod Model.

Blurb

The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand.

The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.

Viatcheslav B. Melas is Professor of Statistics and Numerical Analysis at the St. Petersburg State University and the author of more than one hundred scientific articles and four books. He is an Associate Editor of the Journal of Statistical Planning and Inference and Co-Chair of the organizing committee of the 1^st–5^th St. Petersburg Workshops on Simulation (1994, 1996, 1998, 2001 and 2005).