eprintid: 20808
rev_number: 11
eprint_status: archive
userid: 2326
dir: disk0/00/02/08/08
datestamp: 2016-06-01 13:30:04
lastmod: 2016-08-08 09:24:48
status_changed: 2016-06-01 13:30:04
type: workingPaper
metadata_visibility: show
creators_name: Beran, Rudolf
title: Superefficient Estimation of Multivariate Trend
subjects: ddc-510
divisions: i-110400
keywords: multivariate linear model, deterministic trend, risk estimator, minimum CL, adaptive estimator, Efron-Morris estimator, asymptotic minimax, Pinsker bound
note: überarbeitete Fassung erschienen in: Mathematical Methods of Statistics 8 (1999) 166-180
abstract: The question of recovering a multiband signal from noisy observationsmotivates a model in which the multivariate data points consist of anunknown deterministic trend Xi observed with multivariate Gaussian errors. A cognate random trend model suggests two affineshrinkage estimators for the deterministic trend, which arerelated to an extended Efron-Morris estimator. When represented canonically, the one affineshrinkage estimator performs componentwise James-Stein shrinkage in a coordinate system that is determined by the data. Under the originaldeterministic trend model, this affineshrinkage estimator and its relatives are asymptoticallyminimax in Pinsker's sense over certain classes of subsets of theparameter space. In such fashion, the affineshrinkage estimator and its cousins dominate theclassically efficient least squares estimator. We illustrate their use toimprove on the least squares fit of the multivariate linearmodel.
date: 1998-07
id_scheme: DOI
id_number: 10.11588/heidok.00020808
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 47
ppn_swb: 1657259420
own_urn: urn:nbn:de:bsz:16-heidok-208081
language: eng
bibsort: BERANRUDOLSUPEREFFIC199807
full_text_status: public
place_of_pub: Heidelberg
pages: 16
citation:   Beran, Rudolf  (1998) Superefficient Estimation of Multivariate Trend.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20808/1/beitrag.47.pdf