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

• Autores: Mary C. Meyer
• Localización: Statistical science, ISSN 0883-4237, Vol. 33, Nº. Extra 4, 2018 (Ejemplar dedicado a: Nonparametric Inference Under Shape Constraints), págs. 595-614
• Idioma: inglés
• DOI: 10.1214/18-sts671
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• Resumen

  • Methodology for the partial linear generalized additive model is presented, where components for continuous predictors may bemodeled 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.