Extensions of the Classical Linear Model

Ludwig Fahrmeir, Thomas Kneib, Stefan Lang and Brian Marx
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Ludwig Fahrmeir: University of Munich, Department of Statistics
Thomas Kneib: University of Göttingen, Chair of Statistics
Stefan Lang: University of Innsbruck, Department of Statistics
Brian Marx: Louisiana State University, Experimental Statistics

Chapter 4 in Regression, 2013, pp 177-267 from Springer

Abstract: Abstract This chapter discusses several extensions of the classical linear model. We first describe in Sect. 4.1 the general linear model and its applications. This model allows for correlated errors and heteroscedastic variances of the errors. Section 4.2 discusses several techniques to regularize the least squares estimator. Such a regularization may be useful in cases where the design matrix is highly collinear or even rank deficient. Moreover, regularization techniques allow for built-in variable selection. Section 4.4 describes Bayesian linear models as an alternative to the frequentist linear model framework. In modern statistics, Bayesian approaches have become increasingly more important and widely used.

Keywords: Smoothing Parameter; Ridge Regression; Inclusion Probability; High Posterior Probability; Posterior Model Probability (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-34333-9_4

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DOI: 10.1007/978-3-642-34333-9_4

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