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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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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松緊帶

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

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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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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