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...
| Main Authors: | , , |
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| Format: | Online |
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Universidad Pedagógica y Tecnológica de Colombia
2024
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15586 |
| _version_ | 1801706359026089984 |
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| author | Serna-Morales , Jessica K. Elorza, Mario César Jaramillo Lopera-Gómez, Carlos M. |
| author_facet | Serna-Morales , Jessica K. Elorza, Mario César Jaramillo Lopera-Gómez, Carlos M. |
| author_sort | Serna-Morales , Jessica K. |
| collection | OJS |
| 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. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-15586 |
| institution | Revista Ciencia en Desarrollo |
| publishDate | 2024 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-155862024-05-11T07:17:11Z Comparison of some estimations of Kendall’s t for interval-censored bivariate data Comparación de algunas estimaciones del t de Kendall para datos bivariados con censura a intervalo Serna-Morales , Jessica K. Elorza, Mario César Jaramillo Lopera-Gómez, Carlos M. Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival 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. 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. Universidad Pedagógica y Tecnológica de Colombia 2024-04-09 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15586 10.19053/01217488.v15.n1.2024.15586 Ciencia En Desarrollo; Vol. 15 No. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio Ciencia en Desarrollo; Vol. 15 Núm. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio 2462-7658 0121-7488 |
| spellingShingle | Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival Serna-Morales , Jessica K. Elorza, Mario César Jaramillo Lopera-Gómez, Carlos M. Comparison of some estimations of Kendall’s t for interval-censored bivariate data |
| title | Comparison of some estimations of Kendall’s t for interval-censored bivariate data |
| title_alt | Comparación de algunas estimaciones del t de Kendall para datos bivariados con censura a intervalo |
| 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_short | 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 |
| topic | Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival |
| topic_facet | Cópula medidas de asociación modelo de mezcla Gaussiana supervivencia Association measures copula Gaussian mixture model survival |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15586 |
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