On conditional density estimation

With the aim to mitigate the possibleproblem of negativity in the estimation of the conditionaldensity function, we introduce a so-called re-weightedNadaraya-Watson (RNW) estimator. The proposed RNWestimator is constructed by a slight modificationof the well-known Nadaraya-Watson smoother.Because the estimator is explicitly defined in terms ofthe data, its practical implementation is quite simple.With a detailed asymptotic analysis, we demonstratethat the RNW smoother preserves thesuperior large-sample bias property of thelocal linear smoother of the conditional densityproposed by Fan, Yao and Tong (1996).As a matter of independent statistical interest,the limit distribution of the RNW estimator is alsoderived.