title: Stein Estimation in High Dimensions and the Bootstrap
creator: Beran, Rudolf
subject: ddc-510
subject: 510 Mathematics
description: The Stein estimator and the better positive-part Stein estimatorboth dominate the sample mean, under quadratic loss, in the standardmultivariate model of dimension q. Standard large sample theory does notexplain this phenomenon well. Plausible bootstrap estimators for the riskof the Stein estimator do not converge correctly at the shrinkage point assample size n increases. By analyzing a submodel exactly, with the helpof results from directional statistics, and then letting dimension q go toinfinity, we find:a) In high dimensions, the Stein and positive-part Stein estimators areapproximately admissible and approximately minimax on large compact ballsabout the shrinkage point. The sample mean is neither.b) A new estimator, asymptotically equivalent as dimension q tends toinfinity, appears to dominate the positive-part Stein estimator slightlyfor finite q.c) Resampling from a fitted standard multivariate normal distribution inwhich the length of the fitted mean vector estimates the length of thetrue mean vector well is the key to consistent bootstrap risk estimationfor Stein estimators.
date: 1993-08
type: Working paper
type: info:eu-repo/semantics/workingPaper
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/21410/1/beitrag.01.pdf
identifier: DOI:10.11588/heidok.00021410
identifier: urn:nbn:de:bsz:16-heidok-214106
identifier:   Beran, Rudolf  (1993) Stein Estimation in High Dimensions and the Bootstrap.  [Working paper]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/21410/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng