The Annals of Statistics

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

Sue Leurgans

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Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345711

Digital Object Identifier
doi:10.1214/aos/1176345711

Mathematical Reviews number (MathSciNet)
MR642740

Zentralblatt MATH identifier
0484.62033

JSTOR
links.jstor.org

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

Keywords
Isotonic estimation asymptotic distribution theory

Citation

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


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