Generalized Additive Models, Cubic Splines and Penalized Likelihood.

Abstract

Generalized additive models extended the class of generalized linear models by allowing an arbitrary smooth function for any or all of the covariates. The functions are established by the local scoring procedure, using a smoother as a building block in an iterative algorithm. This paper utilizes a cubic spline smoother in the algorithm and show how the resultant procedure can be view as a method for automatically smoothing a suitably defined partial residual, and more formally, a method for maximizing a penalized likelihood. The authors also examine convergence of the inner (backfitting) loop in this case and illustrate these ideas with some binary response data. Keywords: Spline; Non-parametric regression.

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Document Details

Document Type
Technical Report
Publication Date
May 22, 1987
Accession Number
ADA181773

Entities

People

  • Robert Tibshirani
  • Trevor Hastie

Organizations

  • Stanford University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Algorithms
  • Cancer
  • Computations
  • Convergence
  • Linear Systems
  • Maximum Likelihood Estimation
  • Military Research
  • Neoplasms
  • Ovarian Cancer
  • Predictive Modeling
  • Residuals
  • Statistics
  • United States
  • United States Government
  • Universities
  • Validation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Statistical inference.