TY  - GEN
N2  - 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.
EP  - 19
CY  - Heidelberg
TI  - Bootstrap Variable-Selection and Confidence Sets
AV  - public
ID  - heidok21329
KW  - Coverage probability
KW  -  geometric loss
KW  -  Cp-estimator
A1  - Beran, Rudolf
Y1  - 1994/11//
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/21329/
ER  -