Simultaneous confidence bands for linear and logistic regression models

Abstract

This thesis considers the construction of simultaneous confidence bands for a normal-error linear regression model and a linear logistic regression model with a binary response variable respectively.  For linear regression, three general methods are summarized to construct exact one-sided and two-sided confidence bands over an ellipsoidal restricted region of the predictor space, and they are found to have the equivalent formulae for calculating critical values.  Also, several methods are available to construct confidence bands over a rectangular region.  We compare these methods in terms of the critical value.  For logistic regression, several methods are considered for the construction of confidence bands with or without predictor constraint, which is based on the asymptotic normality of the estimator.  Simulation studies are provided to assess the performance of some key bands.  Several useful conclusions can be drawn.

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