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Estimation and Accuracy after Model Selection

By Bradley Efron

Abstract

Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account. The methodology involves bagging, also known as bootstrap smoothing, to tame the erratic discontinuities of selection-based estimators. A useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators. Two examples, nonparametric and parametric, are carried through in detail: a regression model where the choice of degree (linear, quadratic, cubic,...) is determined by the Cp criterion, and a Lasso-based estimation problem

Topics: model averaging, Cp, Lasso, bagging, bootstrap smoothing, ABC intervals, importance sampling
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.306.6190
Provided by: CiteSeerX
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