Bias-Reduced Simultaneous Confidence Bands on Generalized Linear Models With Restricted Predictor Variables

When multiple inferences on the mean response of a generalized linear model are utilized to make overall decisions, control of the familywise error rate is warranted. Moreover, in many applications, the predictor variable does not span Euclidean space but can reasonably be restricted to a smaller domain. Simultaneous intervals for the mean response of generalized linear models are presented that (1) control the family-wise error rate over a restricted predictor variable space, (2) provide less conservative simultaneous bounds than when utilizing the Scheffé critical value, (3) reduce bias in the interval estimates, and (4) avoid inestimable cases due to separability of the data. Simulations provide evidence that the proposed bias-reduced simultaneous bounds are preferable to MLE-based Scheffé bounds in a wide variety of settings.