| Issue |
ESAIM: PS
Volume 13, January 2009
|
|
|---|---|---|
| Page(s) | 1 - 14 | |
| DOI | https://doi.org/10.1051/ps:2007055 | |
| Published online | 21 February 2009 | |
Asymptotic unbiased density estimators
1
Stochastics Group, Los Alamos National Laboratory, NM 87545, USA.
2
UMR 6625, IRMAR, Université Rennes 2, 35043 France; eml@uhb.fr.
Received:
29
March
2007
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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