Title :Estimation and Inference Methods in Generalized Regression Models with Shape and Order Constraints

Abstract: We consider a generalized regression model with a single response and several predictors, where the relationships between the response and predictors can be specified with shape and smoothness assumptions.  For example, we might know that the probability of diabetes for subjects in a certain population is increasing in age and BMI but decreasing in a fitness measure.    Inference methods for the regression function are derived using theory about projections onto polyhedral convex cones.  Hypothesis tests for the significance of the various predictors and point-wise confidence intervals for the regression function are presented.