A note on the nonparametric estimation of the bivariate distribution under dependent censoring

Author: Ingrid Van Keilegom

Source: Journal of Nonparametric Statistics, Volume 16, Numbers 3-4, Numbers 3-4/June-August 2004 , pp. 659-670(12)

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Abstract:

Consider a random vector (T₁, T₂), and assume that both T₁ and T₂ are subject to random right censoring. We propose new estimators of the bivariate and marginal distributions of T₁ and T₂. The estimators do not require the common assumption of independence between the vector of survival and censoring times, but allow for a certain type of dependent censoring. The proposed estimator of the marginal distribution generalizes the estimator of Cheng (1989). The estimators have intuitive, closed form expressions and are easy to compute. The weak convergence of the estimators is obtained. As an application we discuss the estimation of the regression coefficients in a polynomial regression model, when both the response and the covariate are subject to censoring.

Keywords: Bivariate censoring; Bivariate distribution; Censored covariates; Kernel estimation; Least squares estimation; Marginal distribution; Nonparametric regression; Right censoring

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10485250310001624783

Publication date: 2004-06-01