Density Estimation of Censored Data with Infinite-Order Kernels

Higher-order accurate density estimation under random right censorship is achieved using kernel estimators from a family of infinite-order kernels. A compatible bandwidth selection procedure is also proposed that automatically adapts to level of smoothness of the underlying lifetime density. The combination of infinite-order kernels with the new bandwidth selection procedure produces a considerably improved estimate of the lifetime density and hazard function surpassing the performance of competing estimators. Infinite-order estimators are also utilized in a secondary manner as pilot estimators in the plug-in approach for bandwidth choice in second-order kernels. Simulations illustrate the improved accuracy of the proposed estimator against other nonparametric estimators of the density and hazard function.