Comparison of presmoothing methods in kernel density estimation under censoring (Q142857)

Let \(Y_i\) be the variables of interest, \(C_i\) the censors, and let the observations be \(Z_i=\min(Y_i,C_i)\), \(\delta_i=1_{\{Y_i<C_i\}}\). The authors consider a modification of the Kaplan-Meyer estimator where the censoring indicators \(\delta_i\) are replaced by a smooth nonparametric estimate \(p_i=\hat p(Z_i)\) for \(p(t)=E(\delta_i\,|\,Z_i=t)\). Nadaraya-Watson type, local-linear and local logistic estimates are considered as candidates for \(\hat p(t)\). The asymptotic behavior of the estimates is investigated. Results of simulations and an application to medical data are presented.