Subset Selection in Regression (Chapman & Hall/CRC Monographs on Statistics & Applied Probability) - Hardcover

Miller, Alan

Hardcover

ISBN 10: 0412353806 ISBN 13: 9780412353802

Publisher: Chapman and Hall/CRC, 1990

Synopsis

Most scientific computing packages contain facilities for stepwise regression and often for 'all subsets' and other techniques for finding 'best-fitting' subsets of regression variables. The application of standard theory can be very misleading in such cases when the model has not been chosen a priori, but from the data. There is widespread awareness that considerable over-fitting occurs and that prediction equations obtained after extensive 'data dredging' often perform poorly when applied to new data. This monograph relates almost entirely to least-squares methods of finding and fitting subsets of regression variables, though most of the concepts are presented in terms of the interpretation and statistical properties of orthogonal projections. An early chapter introduces these methods, which are still not widely known to users of least-squares methods. Existing methods are described for testing whether any useful improvement can be obtained by using any of a set of predictors. Spjotvoll's method for comparing two arbitrary subsets of predictor variables is illustrated and described in detail. When the selected model is the 'best-fitting' in some sense, conventional fitting methods give estimates of regression coefficients which are usually biased in the direction of being too large. The extent of this bias is demonstrated for simple cases. Various ad hoc methods for correcting the bias are discussed (ridge regression, James-Stein shrinkage, jack-knifing, etc.), together with the author's maximum likelihood technique. Areas in which further research is needed are also outlined.

About this title

Review

"Overall, this is a fine volume and should be in the possession of all involved in the business of linear regression analysis." -Zentralblatt f]r Mathematik "Miller is to be commended for pulling together a lot of literature...and going straight to the guts of a complex problem. The book is essential reading for anyone doing or pondering research in this area. I also recommend it highly to anyone teaching regression" -Journal of the American Statistical Association

Synopsis

This mongraph presents what is known on estimation, together with some new material, and relates almost entirely to multiple linear regression. The same problems apply to non-linear regression, such as to the fittingof logistic regressions, to the fitting of autoregressive moving average models, or to any situation in which the same data are used both to choose a model and to fit it. The book is not a set of recommendations on how to carry out stepwise regression. It is intended to awaken readers to the dangers in using automatic packages which pick a model and then use least squares to estimate regression coefficients using the same data. It is hoped this monograph will provide the impetus for much-needed research in this area. The volume contains textbook examples, but is not in any sense a complete text on regression.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 1990
• Language: English
• ISBN 10: 0412353806
• ISBN 13: 9780412353802
• Binding: Hardcover
• Edition number: 1
• Number of pages: 240