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1993 | nr 656 | 226
Tytuł artykułu

Statystyczne planowanie eksperymentów w zagadnieniach regresji w warunkach małej próby

Warianty tytułu
Statistical Designing of Experiments in Regression Problems Under Small Sample Conditions
Języki publikacji
Omówiono zagadnienie dotyczące nowoczesnej teorii planowania eksperymentów optymalnych ze względu na wybrane kryterium optymalności.
This monograph contains the essential results of optimal experimental design theory together with a significant number of rather new tools, which are important in applications. In chapter 1 the regression problem is formulated, the experiment for this kind of problem is defined and some introductory examples of experimental design profits are given. In chapter 2 the general linear regression model is described in case of one or more depending variables. The optimal properties of ordinary and generalized least squares method (MLS) are indicated to support MLS as estimation method in linear regression models. Chapter 3 includes a systematic presentation of optimal discrete design theory starting from such notions as experimental region, region of forecast, experimental design, discrete design, information matrix, optimality criterion, optimal design, etc. The equivalence theorem for general convex criterion is given in a form allowing immediate modifications for A-, C-, D-, E-, G-, M- and V-criterion. Some relations between optimal discrete designs and optimal experimental designs are outlined too. The concepts of design efficiency and quasi-optimal design can be found in chapter 4. Several valuable methods of constructing optimal or quasi-optimal designs are given there. Especially various iterative methods and iterative computer algorithms are described, followed by presentation of methods based on designs, which are invariantly optimal under change of experimental (forecast) region or optimality criterion. In chapter 5 one can find a broad review of optimal discrete designs and optimal or quasi-optimal experimental designs for MLS-estimation in case of linear, quadratic, polynomial and trigonometric regression functions of one or more regressors (factors) and several optimality criteria. In a paragraph summaryizing this chapter the benefits from applying optimal designs are outlined. The last chapter 6 deals with experimental design in nonlinear regression models. The main idea of this chapter is to introduce a new kind of optimality criteria for such models. The author calls them relative criteria of global (or local) optimality. The properties of such relative criteria are discussed there. Using relative criteria of global optimality one can obtain that an optimal design coincides in special cases with e.g. mean rank design, minimax rank design, highest mean efficiency design or maximin efficiency design. (original abstract)
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