Comparison of some estimations of Kendall’s t for interval-censored bivariate data
Abstract
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.
Keywords
Association measures, copula, Gaussian mixture model, survival
Author Biography
Mario César Jaramillo Elorza
Escuela de Estadística, Docente
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