Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 109, Issue 507, Pages 991-1007Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2013.823775
Keywords
Bootstrap smoothing; C-p; Importance sampling; ABC intervals; Model averaging; Bagging; Lasso
Categories
Funding
- NIH [8R01 EB002784]
- NSF [DMS 1208787]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1308960] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1208787] Funding Source: National Science Foundation
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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, horizontal ellipsis ) is determined by the C-p criterion and a Lasso-based estimation problem.
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