Some improvements on a boundary corrected kernel density estimator

R. J. Karunamuni; S. Zhang

doi:10.1016/j.spl.2007.09.002

Some improvements on a boundary corrected kernel density estimator

R. J. Karunamuni, S. Zhang

Statistics

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

48 Scopus citations

Abstract

In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this paper, we present a modification to their estimator. We observe that this modification significantly improves the asymptotic bias and variance of their estimator.

Original language	English (US)
Pages (from-to)	499-507
Number of pages	9
Journal	Statistics and Probability Letters
Volume	78
Issue number	5
DOIs	https://doi.org/10.1016/j.spl.2007.09.002
State	Published - Apr 1 2008

Keywords

Density estimation
Kernel density estimation
Mean squared error
Reflection
Transformation boundary effects

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2007.09.002

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title = "Some improvements on a boundary corrected kernel density estimator",

abstract = "In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this paper, we present a modification to their estimator. We observe that this modification significantly improves the asymptotic bias and variance of their estimator.",

keywords = "Density estimation, Kernel density estimation, Mean squared error, Reflection, Transformation boundary effects",

author = "Karunamuni, {R. J.} and S. Zhang",

note = "Funding Information: This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. ",

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AU - Karunamuni, R. J.

AU - Zhang, S.

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PY - 2008/4/1

Y1 - 2008/4/1

N2 - In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this paper, we present a modification to their estimator. We observe that this modification significantly improves the asymptotic bias and variance of their estimator.

AB - In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this paper, we present a modification to their estimator. We observe that this modification significantly improves the asymptotic bias and variance of their estimator.

KW - Density estimation

KW - Kernel density estimation

KW - Mean squared error

KW - Reflection

KW - Transformation boundary effects

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 5

ER -

Some improvements on a boundary corrected kernel density estimator

Abstract

Keywords

ASJC Scopus subject areas

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