
Model Selection and Model Averaging
Hardcover | 29 September 2008
At a Glance
332 Pages
25.4 x 17.78 x 1.91
Hardcover
RRP $157.95
$141.75
10%OFF
or 4 interest-free payments of $35.44 with
orShips in 5 to 7 business days
Industry Reviews
'... given the inviting style of the presentation and the quality of the material, this book could be quite a catch for graduate students as well as for practitioners where models really do make [a] difference.' MAA Reviews
'... the authors have succeeded in bringing together a coherent volume, which gives a state of the art account of the current practice in model selection and comparison, containing a plethora of asymptotic (sometimes new) results, which can be used to compare different model choice criteria. Most importantly, this is the sole volume dedicated to this subject, taking a fully statistical as opposed to an information theoretic approach to the topic of model selection.' Statistics in Society
| Preface | p. xi |
| A guide to notation | p. xiv |
| Model selection: data examples and introduction | p. 1 |
| Introduction | p. 1 |
| Egyptian skull development | p. 3 |
| Who wrote 'The Quiet Don'? | p. 7 |
| Survival data on primary biliary cirrhosis | p. 10 |
| Low birthweight data | p. 13 |
| Football match prediction | p. 15 |
| Speedskating | p. 17 |
| Preview of the following chapters | p. 19 |
| Notes on the literature | p. 20 |
| Akaike's information criterion | p. 22 |
| Information criteria for balancing fit with complexity | p. 22 |
| Maximum likelihood and the Kullback-Leibler distance | p. 23 |
| AIC and the Kullback-Leibler distance | p. 28 |
| Examples and illustrations | p. 32 |
| Takeuchi's model-robust information criterion | p. 43 |
| Corrected AIC for linear regression and autoregressive time series | p. 44 |
| AIC, corrected AIC and bootstrap-AIC for generalised linear models* | p. 46 |
| Behaviour of AIC for moderately misspecified models* | p. 49 |
| Cross-validation | p. 51 |
| Outlier-robust methods | p. 55 |
| Notes on the literature | p. 64 |
| Exercises | p. 66 |
| The Bayesian information criterion | p. 70 |
| Examples and illustrations of the BIC | p. 70 |
| Derivation of the BIC | p. 78 |
| Who wrote 'The Quiet Don'? | p. 82 |
| The BIC and AIC for hazard regression models | p. 85 |
| The deviance information criterion | p. 90 |
| Minimum description length | p. 94 |
| Notes on the literature | p. 96 |
| Exercises | p. 97 |
| A comparison of some selection methods | p. 99 |
| Comparing selectors: consistency, efficiency and parsimony | p. 99 |
| Prototype example: choosing between two normal models | p. 102 |
| Strong consistency and the Hannan-Quinn criterion | p. 106 |
| Mallow's C[subscript p] and its outlier-robust versions | p. 107 |
| Efficiency of a criterion | p. 108 |
| Efficient order selection in an autoregressive process and the FPE | p. 110 |
| Efficient selection of regression variables | p. 111 |
| Rates of convergence* | p. 112 |
| Taking the best of both worlds?* | p. 113 |
| Notes on the literature | p. 114 |
| Exercises | p. 115 |
| Bigger is not always better | p. 117 |
| Some concrete examples | p. 117 |
| Large-sample framework for the problem | p. 119 |
| A precise tolerance limit | p. 124 |
| Tolerance regions around parametric models | p. 126 |
| Computing tolerance thresholds and radii | p. 128 |
| How the 5000-m time influences the 10,000-m time | p. 130 |
| Large-sample calculus for AIC | p. 137 |
| Notes on the literature | p. 140 |
| Exercises | p. 140 |
| The focussed information criterion | p. 145 |
| Estimators and notation in submodels | p. 145 |
| The focussed information criterion, FIC | p. 146 |
| Limit distributions and mean squared errors in submodels | p. 148 |
| A bias-modified FIC | p. 150 |
| Calculation of the FIC | p. 153 |
| Illustrations and applications | p. 154 |
| Exact mean squared error calculations for linear regression* | p. 172 |
| The FIC for Cox proportional hazard regression models | p. 174 |
| Average-FIC | p. 179 |
| A Bayesian focussed information criterion* | p. 183 |
| Notes on the literature | p. 188 |
| Exercises | p. 189 |
| Frequentist and Bayesian model averaging | p. 192 |
| Estimators-post-selection | p. 192 |
| Smooth AIC, smooth BIC and smooth FIC weights | p. 193 |
| Distribution of model average estimators | p. 195 |
| What goes wrong when we ignore model selection? | p. 199 |
| Better confidence intervals | p. 206 |
| Shrinkage, ridge estimation and thresholding | p. 211 |
| Bayesian model averaging | p. 216 |
| A frequentist view of Bayesian model averaging* | p. 220 |
| Bayesian model selection with canonical normal priors* | p. 223 |
| Notes on the literature | p. 224 |
| Exercises | p. 225 |
| Lack-of-fit and goodness-of-fit tests | p. 227 |
| The principle of order selection | p. 227 |
| Asymptotic distribution of the order selection test | p. 229 |
| The probability of overfitting* | p. 232 |
| Score-based tests | p. 236 |
| Two or more covariates | p. 238 |
| Neyman's smooth tests and generalisations | p. 240 |
| A comparison between AIC and the BIC for model testing* | p. 242 |
| Goodness-of-fit monitoring processes for regression models* | p. 243 |
| Notes on the literature | p. 245 |
| Exercises | p. 246 |
| Model selection and averaging schemes in action | p. 248 |
| AIC and BIC selection for Egyptian skull development data | p. 248 |
| Low birthweight data: FIC plots and FIC selection per stratum | p. 252 |
| Survival data on PBC: FIC plots and FIC selection | p. 256 |
| Speedskating data: averaging over covariance structure models | p. 259 |
| Exercises | p. 266 |
| Further topics | p. 269 |
| Model selection in mixed models | p. 269 |
| Boundary parameters | p. 273 |
| Finite-sample corrections* | p. 281 |
| Model selection with missing data | p. 282 |
| When p and q grow with n | p. 284 |
| Notes on the literature | p. 285 |
| Overview of data examples | p. 287 |
| References | p. 293 |
| Author index | p. 306 |
| Subject index | p. 310 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780521852258
ISBN-10: 0521852250
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Published: 29th September 2008
Format: Hardcover
Language: English
Number of Pages: 332
Audience: General Adult
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 25.4 x 17.78 x 1.91
Weight (kg): 0.86
Shipping
| Standard Shipping | Express Shipping | |
|---|---|---|
| Metro postcodes: | $9.99 | $14.95 |
| Regional postcodes: | $9.99 | $14.95 |
| Rural postcodes: | $9.99 | $14.95 |
Orders over $79.00 qualify for free shipping.
How to return your order
At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.
Additional postage charges may be applicable.
Defective items
If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.
For more info please visit our Help Centre.
























