Estimation and Accuracy After Model Selection

• 成果类型: Article
• 署名作者: Efron, Bradley
• 署名单位: Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.823775
• 发表日期: 2014
• 页码: 991-1007
• 关键词: exponential-families; confidence-intervals; Standard errors; bootstrap; Lasso; regression; statistics; supernovae; jackknife; inference

摘要

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.