## The Annals of Statistics

### Consistency in Generalized Isotonic Regression

#### Abstract

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).

#### Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 350-362.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343061

Digital Object Identifier
doi:10.1214/aos/1176343061

Mathematical Reviews number (MathSciNet)
MR365871

Zentralblatt MATH identifier
0305.62044

JSTOR