Asymptotic confidence bands for generalized nonlinear regression models.

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.