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Title: Nonparametric inference for copulas of dependence under length-biased sampling and informative censoring Authors:  Yassir Rabhi - State University of New York (United States)
Taoufik Bouezmarni - Universite de Sherbrooke (Canada) [presenting]
Abstract: Length-biased sampling is common in cross-sectional surveys and prevalent- cohort studies, and is well known to induce bias on the samples variables. The truncation mechanism in such sampling tends to over-select large values and under-select small values of some variables (e.g. lifetime). We consider copulas for modeling the dependence when the collected data are length-biased and subject to informative censoring. For such data, where large values of some variables are more frequent than small ones, modeling the dependence structure without correction leads to biased results. We address nonparametric estimation of the bivariate distribution, copula function and its density, and Kendall and Spearman measures for right-censored length-biased data. The proposed estimator for the bivariate cdf is a Hadamard-differentiable functional of two MLEs (Kaplan-Meier and empirical distributions). Based on this estimator, we devise two estimators for copula function and a local-polynomials estimator for copula density, that accounts for boundary bias. Also, we introduce estimators for Kendall and Spearman measures. The limiting processes of the estimators are established by deriving i.i.d. representations. As by-product, we establish the oscillation behavior of the bivariate cdf estimator.