Parametric and semiparametric estimation methods for bivariate copula in rainfall application

Hydrological phenomena such as drought, flood, and rainfall are one of the natural phenomena that often provide dependent multivariate variables. The correlation of the hydrologic dependent variables can be described by using copula. To determine a specified copula structure that fitted with the mar...

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Main Author:	Mohd. Lokoman, Rahmah
Format:	Thesis
Language:	English
Published:	2017
Subjects:	Q Science (General)
Online Access:	http://eprints.utm.my/id/eprint/91942/1/RahmahMohdLokomanMFS2017.pdf
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id	my-utm-ep.91942
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spelling	my-utm-ep.919422021-08-09T08:46:16Z Parametric and semiparametric estimation methods for bivariate copula in rainfall application 2017 Mohd. Lokoman, Rahmah Q Science (General) Hydrological phenomena such as drought, flood, and rainfall are one of the natural phenomena that often provide dependent multivariate variables. The correlation of the hydrologic dependent variables can be described by using copula. To determine a specified copula structure that fitted with the marginal variables, the copula dependence parameter needs to be estimated. This study focuses on the application of parametric and semiparametric approaches in estimating the copula dependence parameter. The performance of seven parameter estimation methods namely, maximum likelihood (ML) estimation, inference function of margins (IFM), maximization by parts (MBP), pseudo maximum likelihood (PML), the inversion of rank correlation coefficient approach based on Kendall’s tau and Spearman’s rho and maximum likelihood based on kernel density estimation (MLKDE) are compared in the simulation and empirical studies. The simulation and empirical studies are limited to the case of bivariate copulas. The result from the simulation study shows that the parametric approaches are inefficient when the marginal distributions are misspecified. Among the parametric approaches, MBP performs better than MLE and IFM. While, for semiparametric approaches, PML performs well and consistent for any correlation and sample size. The PML can be efficient and consistent with the parametric once the sample size is large. The empirical study is done by applying the estimation methods to identify the dependence of the daily rainfall at two rain gauge stations Station Kuala Krai and Station Ulu Sekor. The result from the empirical study is consistent with the result from the simulation study. Thus, it can be concluded that MBP is preferred when the copula and the marginal distributions are known. While, PML is preferred when the marginal distribution is unknown, where the situation is common in a real data application. 2017 Thesis http://eprints.utm.my/id/eprint/91942/ http://eprints.utm.my/id/eprint/91942/1/RahmahMohdLokomanMFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:132395 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General)
spellingShingle	Q Science (General) Mohd. Lokoman, Rahmah Parametric and semiparametric estimation methods for bivariate copula in rainfall application
description	Hydrological phenomena such as drought, flood, and rainfall are one of the natural phenomena that often provide dependent multivariate variables. The correlation of the hydrologic dependent variables can be described by using copula. To determine a specified copula structure that fitted with the marginal variables, the copula dependence parameter needs to be estimated. This study focuses on the application of parametric and semiparametric approaches in estimating the copula dependence parameter. The performance of seven parameter estimation methods namely, maximum likelihood (ML) estimation, inference function of margins (IFM), maximization by parts (MBP), pseudo maximum likelihood (PML), the inversion of rank correlation coefficient approach based on Kendall’s tau and Spearman’s rho and maximum likelihood based on kernel density estimation (MLKDE) are compared in the simulation and empirical studies. The simulation and empirical studies are limited to the case of bivariate copulas. The result from the simulation study shows that the parametric approaches are inefficient when the marginal distributions are misspecified. Among the parametric approaches, MBP performs better than MLE and IFM. While, for semiparametric approaches, PML performs well and consistent for any correlation and sample size. The PML can be efficient and consistent with the parametric once the sample size is large. The empirical study is done by applying the estimation methods to identify the dependence of the daily rainfall at two rain gauge stations Station Kuala Krai and Station Ulu Sekor. The result from the empirical study is consistent with the result from the simulation study. Thus, it can be concluded that MBP is preferred when the copula and the marginal distributions are known. While, PML is preferred when the marginal distribution is unknown, where the situation is common in a real data application.
format	Thesis
qualification_level	Master's degree
author	Mohd. Lokoman, Rahmah
author_facet	Mohd. Lokoman, Rahmah
author_sort	Mohd. Lokoman, Rahmah
title	Parametric and semiparametric estimation methods for bivariate copula in rainfall application
title_short	Parametric and semiparametric estimation methods for bivariate copula in rainfall application
title_full	Parametric and semiparametric estimation methods for bivariate copula in rainfall application
title_fullStr	Parametric and semiparametric estimation methods for bivariate copula in rainfall application
title_full_unstemmed	Parametric and semiparametric estimation methods for bivariate copula in rainfall application
title_sort	parametric and semiparametric estimation methods for bivariate copula in rainfall application
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/91942/1/RahmahMohdLokomanMFS2017.pdf
_version_	1747818538961207296

Parametric and semiparametric estimation methods for bivariate copula in rainfall application

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