Open Access
September, 1981 A Stochastic Approximation by Observations on a Discrete Lattice Using Isotonic Regression
H. G. Mukerjee
Ann. Statist. 9(5): 1020-1025 (September, 1981). DOI: 10.1214/aos/1176345581

Abstract

A new non-parametric stochastic approximation procedure for estimating the roots of a non-decreasing regression function is described. The observations are taken on a discrete lattice and the estimation is based on the roots of the sample isotonic regression function fitted to the observed values. Asymptotic properties of the estimator are proven. When specialized to the bio-assay case it gives asymptotic results similar to those obtained by Derman for his up-and-down method but under weaker assumptions than Derman required.

Citation

Download Citation

H. G. Mukerjee. "A Stochastic Approximation by Observations on a Discrete Lattice Using Isotonic Regression." Ann. Statist. 9 (5) 1020 - 1025, September, 1981. https://doi.org/10.1214/aos/1176345581

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0478.62069
MathSciNet: MR628757
Digital Object Identifier: 10.1214/aos/1176345581

Subjects:
Primary: 62L20

Keywords: isotonic regression , stochastic approximation

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 5 • September, 1981
Back to Top