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Asymptotic normality of the \(L_1\) error of the Grenander estimator. (English) Zbl 1105.62342
Summary: Groeneboom introduced a jump process that can be used (among other things) to study the asymptotic properties of the Grenander estimator of a monotone density. In this paper we derive the asymptotic normality of a suitably rescaled version of the \(L_1\) error of the Grenander estimator, using properties of this jump process.

62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
62M05 Markov processes: estimation; hidden Markov models
Full Text: DOI Euclid
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