On Conditional Density Estimation

With the aim of mitigating 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. 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 recently proposed in the literature. As a matter of independent statistical interest, the limit distribution of the RNW estimator is also derived.

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