| Functional Approach to Optimal Experimental Design 2006 Edition Contributor(s): Melas, Viatcheslav B. (Author) |
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ISBN: 038798741X ISBN-13: 9780387987415 Publisher: Springer OUR PRICE: $113.05 Product Type: Paperback - Other Formats Published: December 2005 Annotation: The subject of the book is a functional theory of optimal designs elaborated by the author during the last two decades. This theory relates to points and weight of optimal designs considered as functions of some values. For linear models these values are metric characteristics of the set of admissible experimental conditions, for example, the bounds of a segment. For nonlinear models they are true values of the parameter to be estimated. Particularly locally D- optimal designs for exponential regression as an important example of nonlinear models and E-optimal designs for polynomial regression on arbitrary segments will be fully studied. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Medical | Biostatistics - Mathematics | Linear & Nonlinear Programming |
| Dewey: 519.57 |
| LCCN: 2005930803 |
| Series: Lecture Notes in Statistics |
| Physical Information: 0.78" H x 5.83" W x 8.27" (1.00 lbs) 338 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |