Arbeitspapier
A uniform central limit theorem and efficiency for deconvolution estimators
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with square root n rate on the assumption that the smoothness of the functionals is larger than the ill-posedness of the problem, which is given by the polynomial decay rate of the characteristic function of the error. The limit distribution is a generalized Brownian bridge with a covariance structure that depends on the characteristic function of the error and on the functionals. The proposed estimators are optimal in the sense of semiparametric efficiency. The class of linear functionals is wide enough to incorporate the estimation of distribution functions. The proofs are based on smoothed empirical processes and mapping properties of the deconvolution operator.
- Language
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Englisch
- Bibliographic citation
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Series: SFB 649 Discussion Paper ; No. 2012-046
- Classification
-
Wirtschaft
Semiparametric and Nonparametric Methods: General
- Subject
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Deconvolution
Donsker theorem
Efficiency
Distribution function
Smoothed empirical processes
Fourier multiplier
Schätztheorie
Theorie
- Event
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Geistige Schöpfung
- (who)
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Söhl, Jakob
Trabs, Mathias
- Event
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Veröffentlichung
- (who)
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Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
- (where)
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Berlin
- (when)
-
2012
- Handle
- Last update
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10.03.2025, 11:43 AM CET
Data provider
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ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Söhl, Jakob
- Trabs, Mathias
- Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
Time of origin
- 2012
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