Nonparametric estimation of linear functionals of a bivariate distribution under univariate censoring |
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Authors: | Xuewen Lu M.D. Burke |
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Affiliation: | Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4 |
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Abstract: | In the presence of univariate censoring, a class of nonparametric estimators is proposed for linear functionals of a bivariate distribution of paired failure times. The estimators are shown to be root-n consistent and asymptotically normal. An adjusted empirical log-likelihood ratio statistic is developed and proved to follow a chi-square distribution asymptotically. Two types of confidence intervals, based on the normal approximation method and the empirical likelihood method, respectively, are constructed to make inference about the linear functionals. Their performance is evaluated in several simulation studies and a real example. |
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Keywords: | Bivariate distribution Empirical likelihood Linear functional Nonparametric estimation Normal approximation Univariate censoring |
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