Generalized Partially Linear Single-Index Models

R. J. Carroll, Jianqing Fan, Irène Gijbels, M. P. Wand

Research output: Contribution to journalArticle

548 Scopus citations

Abstract

The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination αT0X + βT0Z by η0T0X) + βT0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using local linear methods, we propose estimates of the unknown parameters (α0, β0) and the unknown function η0(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.

Original languageEnglish (US)
Pages (from-to)477-489
Number of pages13
JournalJournal of the American Statistical Association
Volume92
Issue number438
DOIs
StatePublished - Jun 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic theory
  • Generalized linear models
  • Kernel regression
  • Local estimation
  • Local polynomial regression
  • Nonparametric regression
  • Quasi-likelihood

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