Generalized Partially Linear Single-Index Models

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Journal Article
Journal of the American Statistical Association, 1997, 92 (438), pp. 477 - 489
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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 η0(αT0X) + 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. © 1997 Taylor & Francis Group, LLC.
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