On a class of M-estimators for Gaussian long-memory models
On a class of M-estimators for Gaussian long-memory models
No Thumbnail Available
Files
There are no files associated with this item.
Date
1994
Authors
Editors
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
DOI (citable link)
International patent number
Link to the license
EU project number
Project
Open Access publication
Collections
Title in another language
Publication type
Journal article
Publication status
Published in
Biometrika ; 81 (1994), 4. - pp. 755-766. - ISSN 0006-3444
Abstract
We consider estimation for parametric stationary Gaussian models with long memory. The spectral density f(x; θ) is assumed to be characterised by a vector θ = (θ1, θ2, θ3,…, θm) such that θ2 = H ε (½, 1) and f(x; θ) is proportional to x1−2H as x tends to zero. An approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed. Its asymptotic distribution is derived. More generally, the approach leads to a class of M-estimators for which a central limit theorem holds. By choosing an appropriate ψ-function, robustness against additive outliers can be achieved, while keeping high efficiency under the ideal model. This is illustrated by a small simulation study. A simple algorithm and an explicit formula for the efficiency, and thus for choosing an appropriate tuning parameter, are given for Hampel's redescending ψ-function.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Autoregressive,Fractional ARIMA,Influence function,Long-range dependence,Maximum likelihood estimation,Redescending function,Robustness
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690
BERAN, Jan, 1994. On a class of M-estimators for Gaussian long-memory models. In: Biometrika. 81(4), pp. 755-766. ISSN 0006-3444. Available under: doi: 10.1093/biomet/81.4.755BibTex
@article{Beran1994class-18822, year={1994}, doi={10.1093/biomet/81.4.755}, title={On a class of M-estimators for Gaussian long-memory models}, number={4}, volume={81}, issn={0006-3444}, journal={Biometrika}, pages={755--766}, author={Beran, Jan} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/18822"> <dcterms:abstract xml:lang="eng">We consider estimation for parametric stationary Gaussian models with long memory. The spectral density f(x; θ) is assumed to be characterised by a vector θ = (θ1, θ2, θ3,…, θm) such that θ2 = H ε (½, 1) and f(x; θ) is proportional to x1−2H as x tends to zero. An approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed. Its asymptotic distribution is derived. More generally, the approach leads to a class of M-estimators for which a central limit theorem holds. By choosing an appropriate ψ-function, robustness against additive outliers can be achieved, while keeping high efficiency under the ideal model. This is illustrated by a small simulation study. A simple algorithm and an explicit formula for the efficiency, and thus for choosing an appropriate tuning parameter, are given for Hampel's redescending ψ-function.</dcterms:abstract> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/18822"/> <dc:contributor>Beran, Jan</dc:contributor> <dc:language>eng</dc:language> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-03-22T07:11:28Z</dcterms:available> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dcterms:bibliographicCitation>Publ. in: Biometrika ; 81 (1994), 4. - S. 755-766</dcterms:bibliographicCitation> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-03-22T07:11:28Z</dc:date> <dc:rights>terms-of-use</dc:rights> <dc:creator>Beran, Jan</dc:creator> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dcterms:title>On a class of M-estimators for Gaussian long-memory models</dcterms:title> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dcterms:issued>1994</dcterms:issued> </rdf:Description> </rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
No