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