Asymptotic unbiased density estimators

Nicolas W. Hengartner; Éric Matzner-Løber

doi:10.1051/ps:2007055

Asymptotic unbiased density estimators

Nicolas W. Hengartner
, Éric Matzner-Løber

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	ESAIM - Probability and Statistics
Volume	13
DOIs	https://doi.org/10.1051/ps:2007055
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Asymptotic normality
Bias reduction
Confidence intervals
Kernel smoother
Nonparametric density estimation

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10.1051/ps:2007055

Cite this

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abstract = "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.",

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AB - 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.

KW - Asymptotic normality

KW - Bias reduction

KW - Confidence intervals

KW - Kernel smoother

KW - Nonparametric density estimation

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DO - 10.1051/ps:2007055

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JO - ESAIM - Probability and Statistics

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Asymptotic unbiased density estimators

Abstract

Keywords

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