Nonparametric Estimation of Copula Entropy for Left Truncated Right Censored Data
Baby A.K., Rajesh G.
Abstract
In this paper, we investigate nonparametric estimation of copula entropy for bivariate data subject to left truncation
and right censoring (LTRC). A kernel-based estimator of the copula density is constructed under the LTRC
framework, and a plug-in estimator of copula entropy is proposed to measure nonlinear dependence between
variables. The asymptotic properties of the estimator are studied, including bias, variance, consistency, and weak
convergence under suitable regularity conditions. A comprehensive simulation study is conducted under varying
censoring and truncation proportions, sample sizes, and copula families to evaluate the finite-sample performance
of the proposed estimator using measures such as bias and mean squared error. Finally, the methodology is
illustrated through a drought dependence application that involves both drought duration and severity. The results
demonstrate that the proposed estimator effectively captures nonlinear dependence structures under incomplete
survival-type observations.
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