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Titlebook: Linear Models and Design; Jay H. Beder Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer

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发表于 2025-3-21 19:43:10 | 显示全部楼层 |阅读模式
书目名称Linear Models and Design
编辑Jay H. Beder
视频video
概述Guides students using a carefully paced exposition of the theory underlying linear models and experimental design.Provides a resource for researchers seeking a thorough mathematical treatment of the f
图书封面Titlebook: Linear Models and Design;  Jay H. Beder Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer
描述This book is designed as a textbook for graduate students and as a resource for researchers seeking a thorough mathematical treatment of its subject. It develops the main results of regression and the analysis of variance, as well as the central results on confounded and fractional factorial experiments. Matrix theory is deemphasized; its role is taken instead by the theory of linear transformations between vector spaces..The text gives a carefully paced and unified presentation of two topics, linear models and experimental design. Students are assumed to have a solid background in linear algebra, basic knowledge of regression and analysis of variance, and some exposure to experimental design, and should be comfortable with reading and constructing mathematical proofs..The book leads students into the mathematical theory, including many examples both for motivation and for illustration. Over 130 exercises of varying difficulty are included. An extensive mathematical appendix and a detailed index make the text especially accessible..Linear Models and Design. can serve as a textbook for a year-long course in the topics covered, or for a one-semester course in either linear model theo
出版日期Textbook 2022
关键词Linear Models; Design of Experiments; Analysis of Variance; Cell-means Model; Least Squares Estimation; S
版次1
doihttps://doi.org/10.1007/978-3-031-08176-7
isbn_softcover978-3-031-08178-1
isbn_ebook978-3-031-08176-7
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 23:20:31 | 显示全部楼层
searchers seeking a thorough mathematical treatment of the fThis book is designed as a textbook for graduate students and as a resource for researchers seeking a thorough mathematical treatment of its subject. It develops the main results of regression and the analysis of variance, as well as the ce
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Multifactor Designs,there is a method given by multilinear algebra (the Kirkjian-Zelen construction), while for the latter we have a much more complete theory using the arithmetic of finite fields. A goal is to control confounding with blocks, and both cases rest upon some general results on blocking (partitioning of the set of treatment combinations).
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Linear Models,iption of the various ways we will describe linear constraints and linear hypotheses. The latter is given in Lemma 1.33. Note especially the use of subspaces of the parameter space to represent hypotheses.
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Effects in a Factorial Experiment,lattices formed by these hypotheses (see Fig. 2.1) and by their corresponding subspaces. The goal is to clarify the statistical meaning of the hypotheses in terms of the cell means of the experiment. We contrast this with the factor-effects approach, and spend some time showing its relationship with
发表于 2025-3-23 00:06:17 | 显示全部楼层
Estimation,heory of the resulting estimators. It introduces .-tests and .-intervals as well, in anticipation of the next chapter. The Moore-Penrose inverse of the regression/design matrix . also makes its first appearance.
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发表于 2025-3-23 06:54:37 | 显示全部楼层
Fractional Factorial Designs,ns, and what we can do to control the aliasing of effects that automatically results. As in the previous chapter, we study this both in the general setting (arbitrary fractions of arbitrary factorials) and in the special setting of regular fractions in classical symmetric factorials. In the general
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