Statistical Science

A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions

Mary C. Meyer

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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.

Article information

Source
Statist. Sci., Volume 33, Number 4 (2018), 595-614.

Dates
First available in Project Euclid: 29 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.ss/1543482060

Digital Object Identifier
doi:10.1214/18-STS671

Mathematical Reviews number (MathSciNet)
MR3881210

Zentralblatt MATH identifier
07032831

Keywords
Monotone convex partial linear confidence interval

Citation

Meyer, Mary C. A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions. Statist. Sci. 33 (2018), no. 4, 595--614. doi:10.1214/18-STS671. https://projecteuclid.org/euclid.ss/1543482060


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