Partitioning estimation of local variance based on nearest neighbors under censoring

In a nonparametric and heteroscedastic setting, our primary interest is in the local variance estimation when the response variable is subject to right censoring. For the proposed partitioning local variance estimators, based on the first and second nearest neighbors, some transformations on the observed censoring times are involved, using their estimated survival functions. Proofs of consistency and rate of convergence for the presented estimators are given. Moreover, local variance estimation is demonstrated on the basis of real survival data.