Bootstrap Model Selection
Journal article by Jun Shao; Journal of the American Statistical Association, Vol. 91, 1996
Journal Article Excerpt
| Bootstrap Model Selection. by Jun Shao 1. INTRODUCTION In a regression problem, typically there is a vector x of p explanatory variables to be used to fit a model between x and a response variable y. Because some of the components of x may not be related to y, using all p components of x does not necessarily produce a better model than using part of the components of x. Because the relative performance of each model (corresponding to a set of components of x) is usually unknown, we have to select a set of explanatory variables (components of x) based on a data set {([x.sub.i], [y.sub.i]), i = 1,..., n}, where [y.sub.i] is the response at x = [x.sub.i]. This variable selection problem is equivalent to a model selection problem in which each model corresponds to a particular set of the p components of x. There exist many variable/model selection procedures in the case where the relationship between x and y is linear; for example, the Akaike information criterion (AIC) (Akaike 1970); the [C.sub.p] method (Mallows 1973); the Bayes information criterion (BIC) (Hannan and Quinn 1979; Schwartz 1978); the final prediction error ([FPE.sub.[Lambda]]) method (Shibata 1984); the generalized information criterion (Rao and Wu 1989) and its analogs (Potscher 1989); the delete-one cross-validation (Allen 1974; Stone 1974); the generalized cross-validation (Craven and Wahba 1979); and the delete-d cross-validation (Burman 1989; Geisser 1975; Shao 1993; Zhang 1993a). This article introduces some selection methods based on the bootstrap. Besides the theoretical and empirical properties of the bootstrap selection procedures established in this article, there are at least two other reasons to use a bootstrap model selection procedure: 1... |
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