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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.
Dokumententyp: | Arbeitspapier |
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Ort der Veröffentlichung: | Heidelberg |
Erstellungsdatum: | 16 Jun. 2016 07:03 |
Erscheinungsjahr: | November 1994 |
Seitenanzahl: | 19 |
Institute/Einrichtungen: | Fakultät für Mathematik und Informatik > Institut für Mathematik |
DDC-Sachgruppe: | 510 Mathematik |
Freie Schlagwörter: | Coverage probability, geometric loss, Cp-estimator |
Schriftenreihe: | Beiträge zur Statistik > Beiträge |