Estimation and Accuracy after Model Selection.

Area of Science:

• Statistical theory
• Computational statistics
• Econometrics

Background:

• Classical statistical theory often overlooks model selection's impact on estimation accuracy.
• Selection-based estimators can exhibit erratic discontinuities, complicating accuracy assessment.

Purpose of the Study:

• To develop bootstrap methods for computing standard errors and confidence intervals that incorporate model selection.
• To address the challenge of erratic discontinuities in selection-based estimators.

Main Methods:

• Utilizing bagging, also known as bootstrap smoothing, to stabilize selection-based estimators.
• Deriving a new formula for the accuracy of bagging to compute standard errors for smoothed estimators.

Main Results:

• The proposed methods provide accurate standard errors and confidence intervals that account for model selection.
• Bagging effectively tames discontinuities, leading to more reliable estimation accuracy measures.

Conclusions:

• Bootstrap methods, particularly with bagging, offer a robust approach to estimation accuracy when model selection is involved.
• The new bagging accuracy formula enhances the reliability of statistical inference in model selection contexts.