Prediction intervals for GLMs, GAMs, and some survival regression models

David J. Olive, Rasanji C. Rathnayake and Mulubrhan G. Haile

Communications in Statistics - Theory and Methods, 2021, vol. 51, issue 22, 8012-8026

Abstract: Consider a regression model, Y|x∼D(x), where D is a parametric distribution that depends on the p×1 vector of predictors x. Generalized linear models, generalized additive models, and some 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 non parametric shorth prediction interval to Y1*,…,YB* where the Yi* are independent and identically distributed from the distribution D̂(xf) which is a consistent estimator of D(xf). A second prediction interval modifies the shorth prediction interval to work after variable selection and if p > n where n is the sample size. Competing prediction intervals, when they exist, tend to be for one family of D (such as Poisson regression), tend to need n≥10p, and usually have not been proven to work after variable selection.

Date: 2021
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DOI: 10.1080/03610926.2021.1887238

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