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Estimation and accuracy after model selection. (English) Zbl 1368.62071
Summary: 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,\(\ldots\)) is determined by the \(C_p\) criterion and a Lasso-based estimation problem.

MSC:
62F40 Bootstrap, jackknife and other resampling methods
62G09 Nonparametric statistical resampling methods
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J05 Linear regression; mixed models
62J07 Ridge regression; shrinkage estimators (Lasso)
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