eprintid: 21410
rev_number: 12
eprint_status: archive
userid: 2326
dir: disk0/00/02/14/10
datestamp: 2016-06-27 15:06:22
lastmod: 2016-07-22 11:15:14
status_changed: 2016-06-27 15:06:22
type: workingPaper
metadata_visibility: show
creators_name: Beran, Rudolf
title: Stein Estimation in High Dimensions and the Bootstrap
subjects: ddc-510
divisions: i-110400
keywords: Admissible; minimax; high dimension; orthogonal group;
equivariant; directional statistics
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00021410
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 01
ppn_swb: 1657873412
own_urn: urn:nbn:de:bsz:16-heidok-214106
language: eng
bibsort: BERANRUDOLSTEINESTIM199308
full_text_status: public
place_of_pub: Heidelberg
pages: 19
edition: revised August 1993
citation:   Beran, Rudolf  (1993) Stein Estimation in High Dimensions and the Bootstrap.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21410/1/beitrag.01.pdf