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April 2021 The adaptive Wynn algorithm in generalized linear models with univariate response
Fritjof Freise, Norbert Gaffke, Rainer Schwabe
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Ann. Statist. 49(2): 702-722 (April 2021). DOI: 10.1214/20-AOS1974

Abstract

For a nonlinear regression model, the information matrices of designs depend on the parameter of the model. The adaptive Wynn algorithm for D-optimal design estimates the parameter at each step on the basis of the observed responses and employed design points so far, and selects the next design point as in the classical Wynn algorithm for D-optimal design. The name “Wynn algorithm” is in honor of Henry P. Wynn who established the latter “classical” algorithm in his 1970 paper (Ann. Math. Stat. 41 (1970) 1655–1664). The asymptotics of the sequences of designs and maximum likelihood estimates generated by the adaptive algorithm is studied for an important class of nonlinear regression models: generalized linear models whose (univariate) response variables follow a distribution from a one-parameter exponential family. Under the assumptions of compactness of the experimental region and of the parameter space together with some natural continuity assumptions, it is shown that the adaptive ML-estimators are strongly consistent and the design sequence is asymptotically locally D-optimal at the true parameter point. If the true parameter point is an interior point of the parameter space, then under some smoothness assumptions the asymptotic normality of the adaptive ML-estimators is obtained.

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Fritjof Freise. Norbert Gaffke. Rainer Schwabe. "The adaptive Wynn algorithm in generalized linear models with univariate response." Ann. Statist. 49 (2) 702 - 722, April 2021. https://doi.org/10.1214/20-AOS1974

Information

Received: 1 March 2019; Revised: 1 April 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1974

Subjects:
Primary: 62L05
Secondary: 62F12, 62J12

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 2 • April 2021
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