Contents
Preface page xi
A guide to notation xiv

1 Model selection: data examples and introduction
1.1 Introduction
1.2 Egyptian skull development
1.3 Who wrote ‘The Quiet Don’?
1.4 Survival data on primary biliary cirrhosis
1.5 Low birthweight data
1.6 Football match prediction
1.7 Speedskating
1.8 Preview of the following chapters
1.9 Notes on the literature

2 Akaike’s information criterion
2.1 Information criteria for balancing fit with complexity
2.2 Maximum likelihood and the Kullback–Leibler distance
2.3 AIC and the Kullback–Leibler distance
2.4 Examples and illustrations
2.5 Takeuchi’s model-robust information criterion
2.6 Corrected AIC for linear regression and autoregressive time series
2.7 AIC, corrected AIC and bootstrap-AIC for generalised
2.8 Behaviour of AIC for moderately misspecified models
2.9 Cross-validation
2.10 Outlier-robust methods
2.11 Notes on the literature

3 The Bayesian information criterion
3.1 Examples and illustrations of the BIC
3.2 Derivation of the BIC
3.3 Who wrote ‘The Quiet Don’?
3.4 The BIC and AIC for hazard regression models
3.5 The deviance information criterion
3.6 Minimum description length
3.7 Notes on the literature

4 A comparison of some selection methods
4.1 Comparing selectors: consistency, efficiency and parsimony
4.2 Prototype example: choosing between two normal models
4.3 Strong consistency and the Hannan–Quinn criterion
4.4 Mallows’s Cp and its outlier-robust versions
4.5 Efficiency of a criterion
4.6 Efficient order selection in an autoregressive process and the FPE
4.7 Efficient selection of regression variables
4.8 Rates of convergence
4.9 Taking the best of both worlds?
4.10 Notes on the literature

5 Bigger is not always better
5.1 Some concrete examples
5.2 Large-sample framework for the problem
5.3 A precise tolerance limit
5.4 Tolerance regions around parametric models
5.5 Computing tolerance thresholds and radii
5.6 How the 5000-m time influences the 10,000-m time
5.7 Large-sample calculus for AIC
5.8 Notes on the literature

6 The focussed information criterion
6.1 Estimators and notation in submodels
6.2 The focussed information criterion, FIC
6.3 Limit distributions and mean squared errors in submodels
6.4 A bias-modified FIC
6.5 Calculation of the FIC
6.6 Illustrations and applications
6.7 Exact mean squared error calculations for linear regression
6.8 The FIC for Cox proportional hazard regression models
6.9 Average-FIC
6.10 A Bayesian focussed information criterion
6.11 Notes on the literature

7 Frequentist and Bayesian model averaging
7.1 Estimators-post-selection
7.2 Smooth AIC, smooth BIC and smooth FIC weights
7.3 Distribution of model average estimators
7.4 What goes wrong when we ignore model selection?
7.5 Better confidence intervals
7.6 Shrinkage, ridge estimation and thresholding
7.7 Bayesian model averaging
7.8 A frequentist view of Bayesian model averaging
7.9 Bayesian model selection with canonical normal priors
7.10 Notes on the literature

8 Lack-of-fit and goodness-of-fit tests
8.1 The principle of order selection
8.2 Asymptotic distribution of the order selection test
8.3 The probability of overfitting
8.4 Score-based tests
8.5 Two or more covariates
8.6 Neyman’s smooth tests and generalisations
8.7 A comparison between AIC and the BIC for model testing
8.8 Goodness-of-fit monitoring processes for regression models
8.9 Notes on the literature

9 Model selection and averaging schemes in action
9.1 AIC and BIC selection for Egyptian skull development data
9.2 Low birthweight data: FIC plots and FIC selection per stratum
9.3 Survival data on PBC: FIC plots and FIC selection
9.4 Speedskating data: averaging over covariance structure models

10 Further topics
10.1 Model selection in mixed models
10.2 Boundary parameters
10.3 Finite-sample corrections
10.4 Model selection with missing data
10.5 When p and q grow with n
10.6 Notes on the literature

Overview of data examples
References
Author index
Subject index