Open Access
May, 1976 Monotone Percentile Regression
Robert J. Casady, Jonathan D. Cryer
Ann. Statist. 4(3): 532-541 (May, 1976). DOI: 10.1214/aos/1176343459


Suppose that for each number $t$ in [0, 1] there is a distribution with distribution function $F_t(\bullet)$ which has $p$th percentile $\xi(t)$. Consider the problem of estimating $\xi(\bullet)$ under the assumption that $\xi(\bullet)$ is monotone. An estimator which is analogous to the median regression estimator considered in Cryer, Robertson, Wright and Casady (1972), is studied. Asymptotic properties including consistency and law of the iterated logarithm results are obtained under various assumptions.


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Robert J. Casady. Jonathan D. Cryer. "Monotone Percentile Regression." Ann. Statist. 4 (3) 532 - 541, May, 1976.


Published: May, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0361.62027
MathSciNet: MR403050
Digital Object Identifier: 10.1214/aos/1176343459

Primary: 62G05
Secondary: 60F15

Keywords: consistency , Law of the iterated logarithm , monotone regression , percentile estimation

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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