publication . Article . Other literature type . 1992

Submodel selection and evaluation in regression. The X-random case

Breiman, Leo; Spector, Philip;
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  • Published: 01 Dec 1992 Journal: International Statistical Review / Revue Internationale de Statistique, volume 60, page 291 (issn: 0306-7734, Copyright policy)
  • Publisher: JSTOR
Abstract
Summary Often, in a regression situation with many variables, a sequence of submodels is generated containing fewer variables by using such methods as stepwise addition or deletion of variables, or 'best subsets'. The question is which of this sequence of submodels is 'best', and how can submodel performance be evaluated. This was explored in Breiman (1988) for a fixed X-design. This is a sequel exploring the case of random X-designs. Analytical results are difficult, if not impossible. This study involved an extensive simulation. The basis of the study is the theoretical definition of prediction error (PE) as the expected squared error produced by applying a pr...
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