Preview |
PDF, English
Download (135kB) | Terms of use |
Abstract
This paper analyzes estimation by bootstrap variable-selection ina simple Gaussian model where the dimension of the unknown parameter mayexceed that of the data. A naive use of the bootstrap in this problemproduces risk estimators for candidate variable-selections that have astrong upward bias. Resampling from a less overfitted model removes the bias and leads to bootstrap variable-selections that minimize risk asymptotically. A related bootstrap technique generates confidence sets that are centered atthe best bootstrap variable-selection and have two further properties: theasymptotic coverage probability for the unknown parameter is as desired; andthe confidence set is geometrically smaller than a classical competitor.The results suggest a possible approach to confidence sets in other inverseproblems where a regularization technique is used.
Document type: | Working paper |
---|---|
Place of Publication: | Heidelberg |
Date Deposited: | 16 Jun 2016 07:03 |
Date: | November 1994 |
Number of Pages: | 19 |
Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Uncontrolled Keywords: | Coverage probability, geometric loss, Cp-estimator |
Series: | Beiträge zur Statistik > Beiträge |