Subset selection in regression
By: Alan Miller.
Edition: 2nd ed.
Series: Monographs on statistics and applied probability ;; 95
Publisher: Chapman & Hall/CRC
Published: 2002
Place of publication: Boca Raton
Language: eng
Number of pages: 238
Subjects: Regression analysis.; Least squares.
Notes: Includes bibliographical references (p. 223-234) and index.
Table of contents: title: Machine generated contents note: 1 Objectives; title: 1.1 Prediction, explanation, elimination or what?; title: 1.2 How many variables in the prediction formula?; title: 1.3 Alternatives to using subsets; title: 1.4 'Black box' use of best-subsets techniques; title: 2 Least-squares computations; title: 2.1 Using sums of squares and products matrices; title: 2.2 Orthogonal reduction methods; title: 2.3 Gauss-Jordan v. orthogonal reduction methods; title: 2.4 Interpretation of projections; title: Appendix A. Operation counts for all-subsets regression; title: A.1 Garside's Gauss-Jordan algorithm; title: A.2 Planar rotations and a Hamiltonian cycle; title: A.3 Planar rotations and a binary sequence; title: A.4 Fast planar rotations; title: 3 Finding subsets which fit well; title: 3.1 Objectives and limitations of this chapter; title: 3.2 Forward selection; title: 3.3 Efroymson's algorithm; title: 3.4 Backward elimination; title: 3.5 Sequential replacement algorithms; title: 3.6 Replacing two variables at a time; title: 3.7 Genierating all subsets; title: 3.8 Using branch-and-bound techniques; title: 3.9 Grouping variables; title: 3.10 Ridge regression and other alternatives; title: 3.11 The nonnegative garrote and the lasso; title: 3.12 Some examples; title: 3.13 Conclusions and recommendations; title: Appendix A. An algorithm for the lasso; title: 4 Hypothesis testing; title: 4.1 Is there any information in the remaining variables?; title: 4.2 Is one subset better than another?; title: 4.2.1 Applications of Spj-tvoll's method; title: 4.2.2 Using other confidence ellipsoids; title: Appendix A.Spjotvoll's method - detailed description; title: 5 When to stop?; title: 5.1 What criterion should we use?; title: 5.2 Prediction criteria; title: 5.2.1 Mean squared errors of prediction (MSEP); title: 5.2.2 MSEP for the fixed model; title: 5.2.3 MSEP for the random model; title: 5.2.4 A simulation with random predictors; title: 5.3 Cross-validation and the P SS statistic; title: 5.4 Bootstrapping; title: 5.5 Likelihood and information-based stopping rules; title: 5.5.1 Minimum description length (MDL); title: Appendix A. Approximate equivaence of stppingules; title: A.1 F-to-enter; title: A.2 Adjusted R2 or Fisher's A-statistic; title: A.3 Akaikesinformatibn criterion (AIC); title: 6 Estatmaion of regression eficients; title: 6.1 Selection bias; title: 6.2 Choice between two varies; title: 6.3 Selection rduction; title: 6.3.1 Monte C o et tionfias i f d lection; title: 6.3.2 Shrinkage methods; title: 6.3.3 Using the jack-knife; title: 6.3.4 Independent; data sets ;; title: 6.4 Conditional likiood estimations; title: 6.5 Estimationofpopulation means; title: 6.6 Estimating least-squares projections ;; title: Appendix A. Changing projections to equate sums of squares; title: 7 Bayesian mnethods; title: 7.1 Bayesian introduction; title: 7.2 'Spike and slab'prior; title: 7.3 Normal prior for regression coefficients; title: 7.4 Model averaging; title: 7.5 Picking the best model; title: 8 Conclusions and some recommendations; title: References; title: Index.