Geodesic
Asymptotic unbiased density estimators
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 1-14

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n=50, where we see an improvement of as much as 20% over the traditionnal estimator.

DOI : 10.1051/ps:2007055
Classification : 62G07, 62G20
Keywords: nonparametric density estimation, kernel smoother, asymptotic normality, bias reduction, confidence intervals 
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     author = {Hengartner, Nicolas W. and Matzner-L{\o}ber, \'Eric},
     title = {Asymptotic unbiased density estimators},
     journal = {ESAIM: Probability and Statistics},
     pages = {1--14},
     publisher = {EDP-Sciences},
     volume = {13},
     year = {2009},
     doi = {10.1051/ps:2007055},
     mrnumber = {2493852},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007055/}
}
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Hengartner, Nicolas W.; Matzner-Løber, Éric. Asymptotic unbiased density estimators. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 1-14. doi: 10.1051/ps:2007055

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