Volume 13, January 2009
|Page(s)||1 - 14|
|Published online||21 February 2009|
Asymptotic unbiased density estimators
Stochastics Group, Los Alamos National Laboratory, NM 87545, USA.
2 UMR 6625, IRMAR, Université Rennes 2, 35043 France; email@example.com.
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.
Mathematics Subject Classification: 62G07 / 62G20
Key words: Nonparametric density estimation / kernel smoother / asymptotic normality / bias reduction / confidence intervals
© EDP Sciences, SMAI, 2009
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