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November 2018 A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions
Mary C. Meyer
Statist. Sci. 33(4): 595-614 (November 2018). DOI: 10.1214/18-STS671

Abstract

Methodology for the partial linear generalized additive model is presented, where components for continuous predictors may be modeled with shape-constrained regression splines, and components for ordinal predictors may have partial orderings. The estimated mean function is obtained through a projection (or iteratively reweighted projections) onto a polyhedral convex cone; this is key for formally derived inference procedures. Pointwise confidence bands and hypothesis tests for the individual components, as well as a model selection method, are proposed. These methods are available in the R package cgam.

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Mary C. Meyer. "A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions." Statist. Sci. 33 (4) 595 - 614, November 2018. https://doi.org/10.1214/18-STS671

Information

Published: November 2018
First available in Project Euclid: 29 November 2018

zbMATH: 07032831
MathSciNet: MR3881210
Digital Object Identifier: 10.1214/18-STS671

Keywords: Confidence interval , convex , monotone , partial linear

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.33 • No. 4 • November 2018
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