eprintid: 21329
rev_number: 11
eprint_status: archive
userid: 2326
dir: disk0/00/02/13/29
datestamp: 2016-06-16 07:03:01
lastmod: 2016-11-08 18:41:08
status_changed: 2016-06-16 07:03:01
type: workingPaper
metadata_visibility: show
creators_name: Beran, Rudolf
title: Bootstrap Variable-Selection and Confidence Sets
subjects: ddc-510
divisions: i-110400
keywords: Coverage probability, geometric loss, Cp-estimator
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.
date: 1994-11
id_scheme: DOI
id_number: 10.11588/heidok.00021329
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 22
ppn_swb: 165375379X
own_urn: urn:nbn:de:bsz:16-heidok-213290
language: eng
bibsort: BERANRUDOLBOOTSTRAPV199411
full_text_status: public
place_of_pub: Heidelberg
pages: 19
citation:   Beran, Rudolf  (1994) Bootstrap Variable-Selection and Confidence Sets.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21329/1/beitrag.22.pdf