Using a one-parameter model to sequentially estimate the root of a regression function.
type: Item
instance of: scholarly article
title: Using a one-parameter model to sequentially estimate the root of a regression function.
zbMATH Open document ID: 1043.62069
DOI: 10.1016/S0167-9473(99)00107-3
published in: Computational Statistics and Data Analysis
publication date: 2000-10-26T00:00:00Z
review text: This paper considers sequential estimation of the root of a regression function. We explore the possibility of using a one-parameter model to fit data that is collected sequentially and then calculate the value of the design variable for the next observation. This design value itself can serve as an estimator of the root. We find that when the design variable has continuous values, our estimates are consistent. However, when the design variable has discrete values, there are situations in which the estimates can get `stuck' at the wrong value and the method then fails to converge to the correct point. Nonetheless, under certain conditions, we can establish the consistency of the estimates even if the design variable is discrete.
Mathematics Subject Classification ID: 62L12
zbMATH DE Number: 1521709
zbMATH Keywords: Consistency
zbMATH Keywords: sequential design
zbMATH Keywords: stochastic approximation
author: Larry Zaiqian Shen
author: John O'Quigley
MaRDI profile type: Publication
cites work: Q5613647
cites work: Adaptive design and stochastic approximation
cites work: Continual Reassessment Method: A Practical Design for Phase 1 Clinical Trials in Cancer
cites work: A Stochastic Approximation Method
cites work: Q3930489
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Wikidata QID: Q127866181
full work available at URL: s0167-9473(99)00107-3
OpenAlex ID: W2044425309
description: scientific article; zbMATH DE number 1521709