Theory and Methods of Statistics

11.8 Model Selection

In the Gauss-Markov setup one is often concerned with selecting a model from an appropriate class of candidate models. There are a number of methods for model selection and properties of these methods have been investigated by many authors, but we focus on a few of them instead of describing all. Consider the general framework Y = μ + ε, where Y is the n × 1 response vector, μ is the mean vector, and ε is the vector of iid errors with mean 0 and variance σ². We assume that there is a class of candidate models $\left\{{\mathit{X}}_k{\mathit{\beta }}_k:k=1,\dots ,K\right\}$ for describing μ, where X_k is a known n × p_k matrix of rank p_k and β_k is unknown.

11.8.1 An Overview ...