Comparison of some estimations of Kendall’s t for interval-censored bivariate data

Bivariate failure data are common in reliability and survival studies, where estimation of dependency is often an important step in data analysis. In the literature, it known that the correlation coefficients measure the linear relationship between two variables, but strong non-linear relationship c...

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Fecha de publicación:: 2024

Institución:: Universidad Pedagógica y Tecnológica de Colombia

Repositorio:: RiUPTC: Repositorio Institucional UPTC

Idioma:: spa

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network_acronym_str	REPOUPTC2
network_name_str	RiUPTC: Repositorio Institucional UPTC
repository_id_str
spelling	2024-04-092024-07-08T14:24:10Z2024-07-08T14:24:10Zhttps://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/1558610.19053/01217488.v15.n1.2024.15586https://repositorio.uptc.edu.co/handle/001/15389Bivariate failure data are common in reliability and survival studies, where estimation of dependency is often an important step in data analysis. In the literature, it known that the correlation coefficients measure the linear relationship between two variables, but strong non-linear relationship can also exist between them. Kendall's $\tau$ concordance coefficient has become a useful tool for bivariate data analysis, which is used in nonparametric tests of independence and as a complementary measures of association. In the analysis of reliability data, there is a phenomenon that occurs when the value of the lifetime is partially known, which is known as censoring. In this paper, two estimation methods of Kendall's t are compared via simulation, one of them assuming normality in marginal distributions and adjusting them individually and the other based on copulas (Gaussian and Clayton), where the bivariate data are interval censored. The comparison is made using the mean squared error and the median absolute deviation. The results show that the method based on the copula approximation generally produces more precise estimates than the method of individual adjustment of the marginals.Los datos de falla bivariados son comunes en estudios de confiabilidad y supervivencia, donde la estimación de la fuerza de dependencia es a menudo un paso importante en el análisis de los datos. En la literatura, se ha establecido que los coeficientes de correlación miden la relación lineal entre dos variables, pero también pueden existir relaciones no lineales fuertes entre ellas. El coeficiente de concordancia t de Kendall se ha convertido en una herramienta útil para el análisis de datos bivariados, la cual es usada en pruebas no paramétricas de independencia y como una medida complementaria de asociación. En el análisis de datos de confiabilidad, hay un fenómeno que ocurre cuando el valor de las observaciones se conoce parcialmente, lo cual se conoce comocensura. En este trabajo, se comparan vía simulación dos métodos de estimación del t de Kendall, una de ellas suponiendo normalidad en las distribuciones marginales y ajustándolas individualmente, y la otra basada en cópulas (Gaussiana y Clayton), donde los datos bivariados están censurados a intervalo. La comparación se hace mediante el error cuadrático medio y la mediana de la desviación absoluta. Los resultados muestran que el método basado en la aproximación cópula produce en general estimaciones más precisas que el método de ajuste individual de las marginales.spaUniversidad Pedagógica y Tecnológica de ColombiaCiencia En Desarrollo; Vol. 15 No. 1 (2024): Vol 15, Núm.1 (2024): Enero-JunioCiencia en Desarrollo; Vol. 15 Núm. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio2462-76580121-7488Cópulamedidas de asociaciónmodelo de mezcla GaussianasupervivenciaAssociation measurescopulaGaussian mixture modelsurvivalComparison of some estimations of Kendall’s t for interval-censored bivariate dataComparación de algunas estimaciones del t de Kendall para datos bivariados con censura a intervaloinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/access_right/c_abf2Serna-Morales , Jessica K.Jaramillo Elorza, Mario César Lopera-Gómez, Carlos M.001/15389oai:repositorio.uptc.edu.co:001/153892025-07-18 10:56:33.071metadata.onlyhttps://repositorio.uptc.edu.coRepositorio Institucional UPTCrepositorio.uptc@uptc.edu.co
dc.title.en-US.fl_str_mv	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
dc.title.es-ES.fl_str_mv	Comparación de algunas estimaciones del t de Kendall para datos bivariados con censura a intervalo
title	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
spellingShingle	Comparison of some estimations of Kendall’s t for interval-censored bivariate data Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival
title_short	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
title_full	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
title_fullStr	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
title_full_unstemmed	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
title_sort	Comparison of some estimations of Kendall’s t for interval-censored bivariate data
dc.subject.es-ES.fl_str_mv	Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia
topic	Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival
dc.subject.en-US.fl_str_mv	Association measures copula Gaussian mixture model survival
description	Bivariate failure data are common in reliability and survival studies, where estimation of dependency is often an important step in data analysis. In the literature, it known that the correlation coefficients measure the linear relationship between two variables, but strong non-linear relationship can also exist between them. Kendall's $\tau$ concordance coefficient has become a useful tool for bivariate data analysis, which is used in nonparametric tests of independence and as a complementary measures of association. In the analysis of reliability data, there is a phenomenon that occurs when the value of the lifetime is partially known, which is known as censoring. In this paper, two estimation methods of Kendall's t are compared via simulation, one of them assuming normality in marginal distributions and adjusting them individually and the other based on copulas (Gaussian and Clayton), where the bivariate data are interval censored. The comparison is made using the mean squared error and the median absolute deviation. The results show that the method based on the copula approximation generally produces more precise estimates than the method of individual adjustment of the marginals.
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-07-08T14:24:10Z
dc.date.available.none.fl_str_mv	2024-07-08T14:24:10Z
dc.date.none.fl_str_mv	2024-04-09
dc.type.none.fl_str_mv	info:eu-repo/semantics/article
dc.type.coarversion.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv	http://purl.org/coar/resource_type/c_2df8fbb1
dc.identifier.none.fl_str_mv	https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15586 10.19053/01217488.v15.n1.2024.15586
dc.identifier.uri.none.fl_str_mv	https://repositorio.uptc.edu.co/handle/001/15389
url	https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15586 https://repositorio.uptc.edu.co/handle/001/15389
identifier_str_mv	10.19053/01217488.v15.n1.2024.15586
dc.language.iso.none.fl_str_mv	spa
language	spa
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv	http://purl.org/coar/access_right/c_abf2
dc.publisher.es-ES.fl_str_mv	Universidad Pedagógica y Tecnológica de Colombia
dc.source.en-US.fl_str_mv	Ciencia En Desarrollo; Vol. 15 No. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio
dc.source.es-ES.fl_str_mv	Ciencia en Desarrollo; Vol. 15 Núm. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio
dc.source.none.fl_str_mv	2462-7658 0121-7488
institution	Universidad Pedagógica y Tecnológica de Colombia
repository.name.fl_str_mv	Repositorio Institucional UPTC
repository.mail.fl_str_mv	repositorio.uptc@uptc.edu.co
_version_	1839633832684290048

Comparison of some estimations of Kendall’s t for interval-censored bivariate data

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