The Annals of Statistics

Isotonic inverse estimators for nonparametric deconvolution

Geurt Jongbloed, Bert van Es, and Martien van Zuijlen

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A new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems, where the convolution density has one discontinuity. The estimator is shown to be consistent and its cube root asymptotic distribution theory is established. Known results on the minimax risk for the estimation problem indicate the estimator to be efficient.

Article information

Ann. Statist., Volume 26, Number 6 (1998), 2395-2406.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05
Secondary: 62E20: Asymptotic distribution theory

Convex minorant cube root asymptotics isotonic estimation empirical process


van Es, Bert; Jongbloed, Geurt; van Zuijlen, Martien. Isotonic inverse estimators for nonparametric deconvolution. Ann. Statist. 26 (1998), no. 6, 2395--2406. doi:10.1214/aos/1024691476.

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