Selection of the Best Subset in Regression Analysis

By R. R. Hocking, R. Leslie. 1967

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Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso (2017, neutral): “The first two are classical methods in statistics, dating back to at least Beale et al. (1967); Hocking and Leslie (1967) for best subset selection and Efroymson (1966); Draper and Smith (1966) for forward selection; the lasso is (relatively speaking) more recent, due to Tibshirani (1996); Chen et…”
Algorithm for cardinality-constrained quadratic optimization (2009, background): “Authors of [2, 9, 10] use pivoting and enumeration to search for subsets with the best regression “fit” (e.”
Ridge Regression: Applications to Nonorthogonal Problems (1970, methodology): “RIDGE REGRESSION 73 It is interesting to compare how one would handle the subset problem with the RIDGE TRACE and what is obtained from a criterion such as that used by Gorman and Toman [1] and by Hocking and Leslie [2].”
Regressions by Leaps and Bounds (2000, background): “ABRANCHANDBOUNDPROCEDURE A number of authors have described procedures for find- ing the best subset regressions without computing all possible regressions (Hocking and Leslie, 1967; Beale, Kendall and Mann, 1967; LaMotte and Hocking, 1970).”
Some Comments on Cp (2000, methodology): “For k not too large it is feasible ([4], [5], [19]) to compute and display all the 2k+' values of Cp ; for larger values one can use algorithms of [2], [8], [14] to compute only the more interesting (smaller) values.”
The Preference Survey Module: A Validated Instrument for Measuring Risk, Time, and Social Preferences (2016, methodology): “We use a model selection approach, in the spirit of best subset selection (see, e.g., Hocking and Leslie 1967, Bertsimas et al. 2016), which consists of testing all possible combinations of our items using information criteria and then selecting the best model in terms of minimizing mean squared…”
Ridge Regression: Biased Estimation for Nonorthogonal Problems (2000, methodology): “These automatic procedures include regression using the factors obtained from a coordinate transformation using the principal components of X'X, stepwise regression, computation of all 2P regressions, and some subset of all regressions using fractional factorials or a branch and bound technique [3][”