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Bootstrap Variable-Selection and Confidence Sets

Beran, Rudolf

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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.

Item 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 > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Coverage probability, geometric loss, Cp-estimator
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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