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Asymptotic Confidence Bands for Generalized Nonlinear Regression Models

Christopher Cox and Guangqin Ma
Biometrics
Vol. 51, No. 1 (Mar., 1995), pp. 142-150
DOI: 10.2307/2533321
Stable URL: http://www.jstor.org/stable/2533321
Page Count: 9
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Asymptotic Confidence Bands for Generalized Nonlinear Regression Models
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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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