Modeling and estimation of some non Gaussian random fields

In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields wi...

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Detalles Bibliográficos
Autor: Caamaño-Carrillo, Christian Eloy
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2018
País:Chile
OAI Identifier:oai:repositorio.anid.cl:10533/214737
Acceso en línea:https://hdl.handle.net/10533/214737
Access Level:acceso abierto
Palabra clave:Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
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dc.title.es_CL.fl_str_mv Modeling and estimation of some non Gaussian random fields
dc.title.none.fl_str_mv Modeling and estimatión of some non gaussian random fields
title Modeling and estimation of some non Gaussian random fields
spellingShingle Modeling and estimation of some non Gaussian random fields
Caamaño-Carrillo, Christian Eloy
Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
title_short Modeling and estimation of some non Gaussian random fields
title_full Modeling and estimation of some non Gaussian random fields
title_fullStr Modeling and estimation of some non Gaussian random fields
title_full_unstemmed Modeling and estimation of some non Gaussian random fields
title_sort Modeling and estimation of some non Gaussian random fields
dc.creator.none.fl_str_mv Caamaño-Carrillo, Christian Eloy
author Caamaño-Carrillo, Christian Eloy
author_facet Caamaño-Carrillo, Christian Eloy
author_role author
dc.contributor.advisor.none.fl_str_mv Bevilacqua, Moreno
dc.contributor.institution.es_CL.fl_str_mv UNIVERSIDAD DE VALPARAISO
dc.subject.oecd1n.es_CL.fl_str_mv Ingeniería y Tecnología
topic Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
dc.subject.oecd2n.es_CL.fl_str_mv Otras Ingenierías y Tecnologías
dc.subject.oecd3n.es_CL.fl_str_mv Otras Ingenierías y Tecnologías
description In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields with Gamma and Weibull marginals. Both random fields are obtained transforming a rescaled sum of independent copies of squared Gaussian random fields. For the second case, we propose a random field with t marginal distribution. We then consider two possible generalizations allowing for possible asymmetry. In the first approach we obtain a skew-t random field mixing a skew Gaussian random field with an inverse square root Gamma random field. In the second approach we obtain a two piece t random field mixing a specific binary discrete random field with half-t random field. We study the associated second order properties and in the stationary case, the geometrical properties. Since maximum likelihood estimation is computationally unfeasible, even for relatively small data-set, we propose the use of the pairwise likelihood. The effectiveness of our proposal for the gamma and weibull cases, is illustrated through a simulation study and a re-analysis of the Irish Wind speed data (Haslett and Raftery, 1989) without considering any prior transformation of the data as in previous statistical analysis. For the t and asymmetric t cases we present a simulated study in order to show the performance of our method.
publishDate 2018
dc.date.accessioned.none.fl_str_mv 2018-06-18T13:08:40Z
2022-08-23T12:53:59Z
dc.date.available.none.fl_str_mv 2018-06-18T13:08:40Z
2022-08-23T12:53:59Z
dc.date.issued.es_CL.fl_str_mv 2018
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dc.type.tesis.none.fl_str_mv Tesis
format doctoralThesis
status_str publishedVersion
dc.identifier.folio.es_CL.fl_str_mv 21150156
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10533/214737
identifier_str_mv 21150156
url https://hdl.handle.net/10533/214737
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spelling UNIVERSIDAD DE VALPARAISOCaamaño-Carrillo, Christian Eloy2018https://hdl.handle.net/10533/214737http://purl.org/coar/access_right/c_abf2Otras Ingenierías y TecnologíasOtras Ingenierías y TecnologíasIngeniería y TecnologíaModeling and estimation of some non Gaussian random fieldsBevilacqua, MorenoUNIVERSIDAD DE VALPARAISOChileCaamaño-Carrillo, Christian Eloy2018-06-18T13:08:40Z2022-08-23T12:53:59Z2018-06-18T13:08:40Z2022-08-23T12:53:59Z2018In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields with Gamma and Weibull marginals. Both random fields are obtained transforming a rescaled sum of independent copies of squared Gaussian random fields. For the second case, we propose a random field with t marginal distribution. We then consider two possible generalizations allowing for possible asymmetry. In the first approach we obtain a skew-t random field mixing a skew Gaussian random field with an inverse square root Gamma random field. In the second approach we obtain a two piece t random field mixing a specific binary discrete random field with half-t random field. We study the associated second order properties and in the stationary case, the geometrical properties. Since maximum likelihood estimation is computationally unfeasible, even for relatively small data-set, we propose the use of the pairwise likelihood. The effectiveness of our proposal for the gamma and weibull cases, is illustrated through a simulation study and a re-analysis of the Irish Wind speed data (Haslett and Raftery, 1989) without considering any prior transformation of the data as in previous statistical analysis. 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