On Conditional Density Estimation

With the aim to mitigate the possible problem of negativity in the estimation of the conditional density function, we introduce a so-called re-weighted Nadaraya-Watson (RNW) estimator. The proposed RNW estimator is constructed by a slight modification of the well-known Nadaraya-Watson smoother. Because the estimator is explicitly defined in terms of the data, its practical implementation is quite simple. With a detailed asymptotic analysis, we demonstrate that the RNW smoother preserves the superior large-sample bias property of the local linear smoother of the conditional density proposed by Fan, Yao and Tong (1996). As a matter of independent statistical interest, the limit distribution of the RNW estimator is also derived.