eprintid: 20796
rev_number: 13
eprint_status: archive
userid: 2326
dir: disk0/00/02/07/96
datestamp: 2016-05-30 08:47:38
lastmod: 2016-06-21 12:38:45
status_changed: 2016-05-30 08:47:38
type: workingPaper
metadata_visibility: show
creators_name: Franke, Jürgen
creators_name: Kreiss, Jens-Peter
creators_name: Mammen, Enno
creators_name: Neumann, Michael H.
title: Properties of the Nonparametric Autoregressive Bootstrap
subjects: ddc-510
divisions: i-110400
keywords: Bootstrap, nonparametric autoregression, coupling, geometric ergodicity, consistence
note: auch veröffentlicht in: Journal of Time Series Analysis
Volume 23, Issue 5, pages 555–585, September 2002
abstract: We prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. To this end, we revisit this problem for nonparametric autoregressive processes and give some quantitative conditions (i.e., with explicit constants) under which the mixing coefficients of such processes can be bounded by some exponentially decaying sequence. This is achieved by using well-established coupling techniques.Then we apply the result to the bootstrap process and propose some particularestimators of the autoregression function and of the density of the innovations for which the bootstrap process has the desired properties.Moreover, by using some "decoupling" argument, we show that the stationary density of the bootstrap process converges to that of the original process. As an illustration, we use the proposed bootstrap method to construct simultaneous confidence bands and supremum-type tests for the autoregression function as well as to approximate the distribution of the least squares estimator in a certain parametric model.
date: 1998-10-26
id_scheme: DOI
id_number: 10.11588/heidok.00020796
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 52
ppn_swb: 1657248097
own_urn: urn:nbn:de:bsz:16-heidok-207960
language: eng
bibsort: FRANKEJURGPROPERTIES19981026
full_text_status: public
place_of_pub: Heidelberg
pages: 26
citation:   Franke, Jürgen ; Kreiss, Jens-Peter ; Mammen, Enno ; Neumann, Michael H.  (1998) Properties of the Nonparametric Autoregressive Bootstrap.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20796/1/beitrag.52.pdf