Characteristic function-based semiparametric inference for skew-symmetric models

Handle URI:
http://hdl.handle.net/10754/562468
Title:
Characteristic function-based semiparametric inference for skew-symmetric models
Authors:
Potgieter, Cornelis J.; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
Skew-symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified skew-symmetric distribution. The estimation of the location and scale parameters corresponding to the symmetric component is considered here, with the symmetric component known. Emphasis is placed on using the empirical characteristic function to estimate these parameters. This is made possible by an invariance property of the skew-symmetric family of distributions, namely that even transformations of random variables that are skew-symmetric have a distribution only depending on the symmetric density. A distance metric between the real components of the empirical and true characteristic functions is minimized to obtain the estimators. The method is semiparametric, in that the symmetric component is specified, but the skewing function is assumed unknown. Furthermore, the methodology is extended to hypothesis testing. Two tests for a hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation of these tests. The outcomes of various numerical experiments are presented. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Spatio-Temporal Statistics and Data Analysis Group
Publisher:
Wiley-Blackwell
Journal:
Scandinavian Journal of Statistics
Issue Date:
26-Dec-2012
DOI:
10.1111/j.1467-9469.2012.00822.x
Type:
Article
ISSN:
03036898
Sponsors:
This research was supported by NSF grants DMS-1007504 and DMS-0914951, and also by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPotgieter, Cornelis J.en
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2015-08-03T10:39:19Zen
dc.date.available2015-08-03T10:39:19Zen
dc.date.issued2012-12-26en
dc.identifier.issn03036898en
dc.identifier.doi10.1111/j.1467-9469.2012.00822.xen
dc.identifier.urihttp://hdl.handle.net/10754/562468en
dc.description.abstractSkew-symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified skew-symmetric distribution. The estimation of the location and scale parameters corresponding to the symmetric component is considered here, with the symmetric component known. Emphasis is placed on using the empirical characteristic function to estimate these parameters. This is made possible by an invariance property of the skew-symmetric family of distributions, namely that even transformations of random variables that are skew-symmetric have a distribution only depending on the symmetric density. A distance metric between the real components of the empirical and true characteristic functions is minimized to obtain the estimators. The method is semiparametric, in that the symmetric component is specified, but the skewing function is assumed unknown. Furthermore, the methodology is extended to hypothesis testing. Two tests for a hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation of these tests. The outcomes of various numerical experiments are presented. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.en
dc.description.sponsorshipThis research was supported by NSF grants DMS-1007504 and DMS-0914951, and also by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectAsymmetryen
dc.subjectCharacteristic functionen
dc.subjectDistributional invarianceen
dc.subjectHypothesis testingen
dc.subjectSemiparametric inferenceen
dc.subjectSkew-symmetric distributionen
dc.titleCharacteristic function-based semiparametric inference for skew-symmetric modelsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Groupen
dc.identifier.journalScandinavian Journal of Statisticsen
dc.contributor.institutionDepartment of Statistical Science, Southern Methodist University, United Statesen
kaust.authorGenton, Marc G.en
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