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

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
Mots clés : nonparametric density estimation, kernel smoother, asymptotic normality, bias reduction, confidence intervals 
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     title = {Asymptotic unbiased density estimators},
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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. http://archive.numdam.org/articles/10.1051/ps:2007055/

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