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March, 1975 Consistency in Generalized Isotonic Regression
Tim Robertson, F. T. Wright
Ann. Statist. 3(2): 350-362 (March, 1975). DOI: 10.1214/aos/1176343061


Suppose $T$ is a partially ordered set and that associated with each $t$ in $T$ we have a distribution with "location parameter" $m(t)$. In this paper we discuss consistency properties of estimates of $m(\cdot)$ which are isotonic with respect to a partial order. The results extend results in the literature, some of which are contained in Brunk (1970) (Estimation of isotonic regression in Nonparametric Techniques in Statistical Inference, Cambridge University Press, 177-195), Cryer, et al. (1972) (Monotone median regression in Ann. Math. Statist. 43), Hanson, et al. (1973) (On consistency in monotone regression in Ann. Statist. 1), and Robertson and Wright (1973) (Multiple istonic median regression in Ann. Statist. 1).


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Tim Robertson. F. T. Wright. "Consistency in Generalized Isotonic Regression." Ann. Statist. 3 (2) 350 - 362, March, 1975.


Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0305.62044
MathSciNet: MR365871
Digital Object Identifier: 10.1214/aos/1176343061

Primary: 60F05
Secondary: 60F15 , 62G05

Keywords: consistency , exponential rates of convergence , isotonic regression

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 2 • March, 1975
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