Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model

For a conditional density function (CDF) in the right-censored model, the local linear (LL) estimator has superior bias properties compared with the Nadaraya-Watson (NW) one, but it may have negative values and thus give rise to unsuitable inference. In order to alleviate the possible negativity of the LL estimator, we define a reweighted NW (RNW) estimator of the CDF in the right-censored model by employing the empirical likelihood (EL) method. The RNW estimator is constructed by modifying the NW estimator slightly, so it naturally inherits the nonnegativity of the NW one. It is assumed that the censoring time is independent of the survival time with the associated covariate. Under stationary alpha-mixing observations, the weak consistency and asymptotic normality of the RNW estimator are developed. The asymptotic normality shows that the RNW estimator possesses the bias and variance of the LL estimator. Finally, we conduct simulations to evaluate the finite sample performance of the estimator. (C) 2020 Elsevier B.V. All rights reserved.