Asymptotic normality of nonparametric kernel type deconvolution density estimators: Crossing the cauchy boundary

A. J. Van Es; H. W. Uh

doi:10.1080/10485250310001644574

Asymptotic normality of nonparametric kernel type deconvolution density estimators: Crossing the cauchy boundary

A. J. Van Es^*, H. W. Uh

^*Corresponding author for this work

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

18 Citations (Scopus)

Abstract

We derive asymptotic normality of kernel type deconvolution density estimators. In particular, we consider deconvolution problems where the known component of the convolution has a symmetric λ-stable distribution with 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value 1, the case of Cauchy deconvolution.

Original language	English
Pages (from-to)	261-277
Number of pages	17
Journal	Journal of Nonparametric Statistics
Volume	16
Issue number	1-2
DOIs	https://doi.org/10.1080/10485250310001644574
Publication status	Published - Feb 2004
Externally published	Yes

Keywords

Asymptotic normality
Deconvolution
Kernel estimation

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10.1080/10485250310001644574

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title = "Asymptotic normality of nonparametric kernel type deconvolution density estimators: Crossing the cauchy boundary",

abstract = "We derive asymptotic normality of kernel type deconvolution density estimators. In particular, we consider deconvolution problems where the known component of the convolution has a symmetric λ-stable distribution with 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value 1, the case of Cauchy deconvolution.",

keywords = "Asymptotic normality, Deconvolution, Kernel estimation",

author = "\{Van Es\}, \{A. J.\} and Uh, \{H. W.\}",

note = "Funding Information: The research of the second author has been financed by the Netherlands Organization for the Advancement of Scientific Research (NWO). This article consists of a part of the Ph.D. thesis of H.-W. Uh at the University of Amsterdam. We would like to thank one of the referees whose thorough reading of the original manuscript and subsequent remarks has tremendously improved the readability of the article.",

year = "2004",

month = feb,

doi = "10.1080/10485250310001644574",

language = "English",

volume = "16",

pages = "261--277",

journal = "Journal of Nonparametric Statistics",

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publisher = "Taylor and Francis Ltd.",

number = "1-2",

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TY - JOUR

T1 - Asymptotic normality of nonparametric kernel type deconvolution density estimators

T2 - Crossing the cauchy boundary

AU - Van Es, A. J.

AU - Uh, H. W.

N1 - Funding Information: The research of the second author has been financed by the Netherlands Organization for the Advancement of Scientific Research (NWO). This article consists of a part of the Ph.D. thesis of H.-W. Uh at the University of Amsterdam. We would like to thank one of the referees whose thorough reading of the original manuscript and subsequent remarks has tremendously improved the readability of the article.

PY - 2004/2

Y1 - 2004/2

N2 - We derive asymptotic normality of kernel type deconvolution density estimators. In particular, we consider deconvolution problems where the known component of the convolution has a symmetric λ-stable distribution with 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value 1, the case of Cauchy deconvolution.

AB - We derive asymptotic normality of kernel type deconvolution density estimators. In particular, we consider deconvolution problems where the known component of the convolution has a symmetric λ-stable distribution with 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value 1, the case of Cauchy deconvolution.

KW - Asymptotic normality

KW - Deconvolution

KW - Kernel estimation

UR - https://www.scopus.com/pages/publications/0442313365

U2 - 10.1080/10485250310001644574

DO - 10.1080/10485250310001644574

M3 - Article

AN - SCOPUS:0442313365

SN - 1048-5252

VL - 16

SP - 261

EP - 277

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

IS - 1-2

ER -

Asymptotic normality of nonparametric kernel type deconvolution density estimators: Crossing the cauchy boundary

Abstract

Keywords

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