Subset Selection in Regression

Subset Selection in Regression

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Originally published in 1990, the first edition of Subset Selection in Regression filled a significant gap in the literature, and its critical and popular success has continued for more than a decade. Thoroughly revised to reflect progress in theory, methods, and computing power, the second edition promises to continue that tradition. The author has thoroughly updated each chapter, incorporated new material on recent developments, and included more examples and references. New in the Second Edition: * A separate chapter on Bayesian methods * Complete revision of the chapter on estimation * A major example from the field of near infrared spectroscopy * More emphasis on cross-validation * Greater focus on bootstrapping * Stochastic algorithms for finding good subsets from large numbers of predictors when an exhaustive search is not feasible * Software available on the Internet for implementing many of the algorithms presented * More examples Subset Selection in Regression, Second Edition remains dedicated to the techniques for fitting and choosing models that are linear in their parameters and to understanding and correcting the bias introduced by selecting a model that fits only slightly better than others. The presentation is clear, concise, and belongs on the shelf of anyone researching, using, or teaching subset selecting techniques.show more

Product details

  • Hardback | 256 pages
  • 154.9 x 231.1 x 20.3mm | 453.6g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 19 black & white illustrations
  • 1584881712
  • 9781584881711
  • 1,888,026

Review quote

"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 Associationshow more

Table of contents

OBJECTIVES Prediction, Explanation, Elimination or What? How Many Variables in the Prediction Formula? Alternatives to Using Subsets 'Black Box' Use of Best-Subsets Techniques LEAST-SQUARES COMPUTATIONS Using Sums of Squares and Products Matrices Orthogonal Reduction Methods Gauss-Jordan v. Orthogonal Reduction Methods Interpretation of Projections Appendix A: Operation Counts for All-Subsets Regression FINDING SUBSETS WHICH FIT WELL Objectives and Limitations of this Chapter Forward Selection Efroymson's Algorithm Backward Elimination Sequential Replacement Algorithm Replacing Two Variables at a Time Generating All Subsets Using Branch-and-Bound Techniques Grouping Variables Ridge Regression and Other Alternatives The Non-Negative Garrote and the Lasso Some Examples Conclusions and Recommendations HYPOTHESIS TESTING Is There any Information in the Remaining Variables? Is One Subset Better than Another? Appendix A: Spjftvoll's Method - Detailed Description WHEN TO STOP? What Criterion Should We Use? Prediction Criteria Cross-Validation and the PRESS Statistic Bootstrapping Likelihood and Information-Based Stopping Rules Appendix A. Approximate Equivalence of Stopping Rules ESTIMATION OF REGRESSION COEFFICIENTS Selection Bias Choice Between Two Variables Selection Bias in the General Case, and its Reduction Conditional Likelihood Estimation Estimation of Population Means Estimating Least-Squares Projections Appendix A: Changing Projections to Equate Sums of Squares BAYESIAN METHODS Bayesian Introduction 'Spike and Slab' Prior Normal prior for Regression Coefficients Model Averaging Picking the Best Model CONCLUSIONS AND SOME RECOMMENDATIONS REFERENCES INDEXshow more

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