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Book Series Springer Texts in Statistics Volume 0 / 2010 to Volume 120 / 2013

Book Plane Answers to Complex Questions The Theory of Linear Models

Book Statistical Learning from a Regression Perspective

Chapter General Gauss–Markov Models The standard linear model assumes the data vector has a covariance matrix of \(\sigma ^2 I\). Sections 2.7 and 3.8 extended the theory to having a covariance matrix of \(\sigma ^2 V\) where V was known and positi...

Chapter Model Diagnostics This chapter focuses on methods for evaluating the assumptions made in a standard linear model and on the use of transformations to correct such problems.

Chapter Estimation This chapter focuses on the theory of least squares estimation. It begins with a discussion of identifiability and estimability. It includes discussion of generalized least squares estimation and the possible ...

Chapter Variable Selection This chapter addresses the question of which predictor variables should be included in a linear model. The easiest version of the problem is, given a linear model, which variables should be excluded. To that e...

Chapter One-Way ANOVA This chapter considers the analysis of the one-way ANOVA models originally exploited R.A. Fisher.

Chapter Statistical Learning as a Regression Problem This chapter makes four introductory points: (1) regression analysis is defined by the conditional distribution of Y |X, not by a conventional linear regression model; (2) different forms of regression analysis a...

Chapter Regression Analysis Francis Galton, a half-cousin of Charles Darwin, is often credited as the founder of regression analysis, a tool he used for studying heredity and the social sciences. R.A. seems to be responsible for our cu...

Chapter Classification and Regression Trees (CART) In this chapter, we turn to recursive partitioning, which comes in various forms including decision trees and classification and regression trees (CART). We will see that the algorithmic machinery successively...

Chapter Experimental Design Models In this chapter we examine three models used to analyze results obtained from three specific experimental designs. The designs are the completely randomized design, the randomized complete block design, and th...

Chapter Random Forests This chapter continues to build on the idea of ensembles of statistical learning procedures. Random forests is introduced, which is an extremely useful approach that extends and improves on bagging. As before,...

Chapter Support Vector Machines Support vector machines perhaps has the best mathematical pedigree of any statistical learning procedure. It was originally developed as a classifier that maximizes a somewhat different definition of a margin,...

Chapter Reinforcement Learning and Genetic Algorithms There are a wide variety of empirical settings that do not easily fit within an optimization framework and for which results that are “good,” but not necessarily the “best,” are the only practical option. When...

Chapter Split Plot Models This chapter introduces a cluster sampling model and then adapts that model to develop generalizations of split plot models. Split plot models are among the simplest of the mixed models considered in ALM-III in t...

Chapter Introduction This chapter introduces the general linear model, illustrating how it subsumes a variety of standard applied models. It also introduces random vectors and matrices and the distributions that will be used with ...

Chapter Collinearity and Alternative Estimates This chapter deals with problems caused by having predictor variables that are very nearly redundant. It examines estimation methods developed for dealing with those problems and then goes on to introduce a va...

Chapter Testing This chapter considers two approaches to testing linear models. The approaches are identical in that a test under either approach is a well-defined test under the other. The two methods differ only conceptuall...