Date of Award

5-1-2019

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Olive, David

Abstract

Consider a regression model where Y|x ∼ D(h(x),θ) for some real valued function such as h(x) = xTβ where D is a parametric distribution that depends on x only through h(x). Several important generalized linear models, generalized additive models, and survival regression models have this form. To obtain a prediction interval for a future value of the response variable Yf given a vector of predictors xf, apply the nonparametric shorth prediction interval to Y ∗ 1 ,...,Y ∗ B where the Y ∗ i are independent and identically distributed from the distribution D(ˆ h(xf), ˆ θ). These prediction intervals can also work after variable or model selection.

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