Abstract 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 α − 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.

中文翻译：

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右删失模型中条件密度函数的重新加权 Nadaraya-Watson 估计

摘要 对于右删失模型中的条件密度函数 (CDF)，局部线性 (LL) 估计量与 Nadaraya-Watson (NW) 估计量相比具有更好的偏置特性，但它可能具有负值，从而导致不合适推理。为了减轻 LL 估计量的可能负性，我们通过采用经验似然 (EL) 方法在右删失模型中定义了 CDF 的重新加权 NW (RNW) 估计量。RNW 估计量是通过对 NW 估计量稍加修改而构建的，因此它自然地继承了 NW 估计量的非负性。假设审查时间与相关协变量的生存时间无关。在平稳的 α - 混合观测下，RNW 估计量的弱一致性和渐近正态性得到了发展。渐近正态性表明 RNW 估计量具有 LL 估计量的偏差和方差。最后，我们进行模拟以评估估计器的有限样本性能。