The Annals of Statistics

Asymptotic Distributions of Slope-of-Greatest-Convex-Minorant Estimators

Sue Leurgans

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Isotonic estimation involves the estimation of a function which is known to be increasing with respect to a specified partial order. For the case of a linear order, a general theorem is given which simplifies and extends the techniques of Prakasa Rao and Brunk. Sufficient conditions for a specified limit distribution to obtain are expressed in terms of a local condition and a global condition. It is shown that the rate of convergence depends on the order of the first non-zero derivative and that this result can obtain even if the function is not monotone over its entire domain. The theorem is applied to give the asymptotic distributions of several estimators.

Article information

Ann. Statist., Volume 10, Number 1 (1982), 287-296.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 62G05: Estimation 62G20: Asymptotic properties

Isotonic estimation asymptotic distribution theory


Leurgans, Sue. Asymptotic Distributions of Slope-of-Greatest-Convex-Minorant Estimators. Ann. Statist. 10 (1982), no. 1, 287--296. doi:10.1214/aos/1176345711.

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