Adaptive quantile estimation in deconvolution with unknown error distribution

Itai Dattner; Markus Reiß; Mathias Trabs

doi:10.3150/14-BEJ626

Adaptive quantile estimation in deconvolution with unknown error distribution

Itai Dattner, Markus Reiß, Mathias Trabs

Department of Statistics

University of Haifa

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

Abstract

Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.

Original language	American English
Pages (from-to)	143-192
Number of pages	50
Journal	Bernoulli
Volume	22
Issue number	1
DOIs	https://doi.org/10.3150/14-BEJ626
State	Published - Feb 2016

Keywords

Adaptive estimation
Deconvolution
Distribution function
Minimax convergence rates
Plug-in estimator
Quantile function
Random fourier multiplier

All Science Journal Classification (ASJC) codes

Statistics and Probability

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10.3150/14-BEJ626

Cite this

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title = "Adaptive quantile estimation in deconvolution with unknown error distribution",

abstract = "Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.",

keywords = "Adaptive estimation, Deconvolution, Distribution function, Minimax convergence rates, Plug-in estimator, Quantile function, Random fourier multiplier",

author = "Itai Dattner and Markus Rei{\ss} and Mathias Trabs",

note = "Funding Information: This research started when the first author was a Postdoc at EURANDOM, Eindhoven University of Technology, The Netherlands. The research was partly supported by the Deutsche Forschungsgemeinschaft through the FOR 1735 Structural Inference in Statistics. Part of the work on this project was done during a visit of the third author to EURANDOM. We thank three anonymous referees for helpful comments and suggestions.",

year = "2016",

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doi = "10.3150/14-BEJ626",

language = "American English",

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T1 - Adaptive quantile estimation in deconvolution with unknown error distribution

AU - Dattner, Itai

AU - Reiß, Markus

AU - Trabs, Mathias

N1 - Funding Information: This research started when the first author was a Postdoc at EURANDOM, Eindhoven University of Technology, The Netherlands. The research was partly supported by the Deutsche Forschungsgemeinschaft through the FOR 1735 Structural Inference in Statistics. Part of the work on this project was done during a visit of the third author to EURANDOM. We thank three anonymous referees for helpful comments and suggestions.

PY - 2016/2

Y1 - 2016/2

N2 - Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.

AB - Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.

KW - Adaptive estimation

KW - Deconvolution

KW - Distribution function

KW - Minimax convergence rates

KW - Plug-in estimator

KW - Quantile function

KW - Random fourier multiplier

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U2 - 10.3150/14-BEJ626

DO - 10.3150/14-BEJ626

M3 - Article

SN - 1350-7265

VL - 22

SP - 143

EP - 192

JO - Bernoulli

JF - Bernoulli

IS - 1

ER -

Adaptive quantile estimation in deconvolution with unknown error distribution

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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