Open Access
March, 1982 Monotone Regression Estimates for Grouped Observations
F. T. Wright
Ann. Statist. 10(1): 278-286 (March, 1982). DOI: 10.1214/aos/1176345710


The maximum likelihood estimator of a nondecreasing regression function with normally distributed errors has been considered in the literature. Its asymptotic distribution at a point is related to a solution of the heat equation, and its rate of convergence to the underlying regression function is of order $n^{-1/3}$. This estimator can be modified by grouping adjacent observations and then "isotonizing" the corresponding means. It is shown that the resulting estimator has an asymptotic normal distribution for certain group sizes and its rate of convergence is of order $n^{-2/5}$. The results of a simulation study for small sample sizes are presented and grouping procedures are discussed.


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F. T. Wright. "Monotone Regression Estimates for Grouped Observations." Ann. Statist. 10 (1) 278 - 286, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0494.62031
MathSciNet: MR642739
Digital Object Identifier: 10.1214/aos/1176345710

Primary: 62F10
Secondary: 62E20

Keywords: asymptotic distribution and rates of convergence , grouped observations , interpolation , isotone regression

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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