Asymptotic confidence bands for generalized nonlinear regression models
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Updated: Sep 23, 2026

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Published on: October 23, 2020
1Department of Biostatistics, University of Rochester Medical Center, New York 14642, USA.
Abstract:
Asymptotic confidence bands for generalized nonlinear regression models are developed. These are based on a combination of the S method of Scheffe, together with the delta method which is used to approximate the mean function by a linear combination of the parameters. The approach can be used in any situation where large sample theory can be applied to yield asymptotically normal estimates of the parameters, together with a consistent estimate of the large sample covariance matrix. Alternative formulations for various special cases allow the use of restricted range bands. A number of examples are given, including a pharmacokinetic model, a logit model with a background response rate, and a parametric survival model.
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