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On Conditional Density Estimation
Author(s) -
De Gooijer Jan G.,
Zerom Dawit
Publication year - 2003
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00226
Subject(s) - estimator , mathematics , conditional probability distribution , conditional expectation , asymptotic distribution , density estimation , limit (mathematics) , statistics , mathematical analysis
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.