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

Stochastics Group
MST-8, Los Alamos National Laboratory
Université de Rennes 2

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

7 Citations (Scopus)

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

Access to Document

10.1051/ps:2007055

Cite this

@article{a8bf0a5a84ae4904842b270d702e0097,

title = "Asymptotic unbiased density estimators",

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.",

keywords = "Asymptotic normality, Bias reduction, Confidence intervals, Kernel smoother, Nonparametric density estimation",

author = "Hengartner, \{Nicolas W.\} and {\'E}ric Matzner-L{\o}ber",

year = "2009",

month = jan,

day = "1",

doi = "10.1051/ps:2007055",

language = "English",

volume = "13",

pages = "1--14",

journal = "ESAIM - Probability and Statistics",

issn = "1292-8100",

publisher = "EDP Sciences",

}

TY - JOUR

T1 - Asymptotic unbiased density estimators

AU - Hengartner, Nicolas W.

AU - Matzner-Løber, Éric

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

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

U2 - 10.1051/ps:2007055

DO - 10.1051/ps:2007055

M3 - Article

AN - SCOPUS:68349135620

SN - 1292-8100

VL - 13

SP - 1

EP - 14

JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

ER -

Asymptotic unbiased density estimators

Abstract

Keywords

Access to Document

Fingerprint

Cite this