University of Cincinnati Lindner College of Business

Penalized Spline Estimation for Generalized Partially Linear Single-Index Models
Yan Yu

Status: Published
Year: 2017
Publication Name: Statistics and Computing
Volume: 27, Issue: 2, Page Number(s): 571-582


Generalised linear models are frequently used in modeling the relationship of the response variable from the general exponential family with a set of predictor variables, where a linear combination of predictors is linked to the mean of the response variable. We propose a penalised spline (P-spline) estimation for generalised partially linear single-index models, which extend the generalised linear models to include nonlinear effect for some predictors. The proposed models can allow flexible dependence on some predictors while overcome the "curse of dimensionality". We investigate the P-spline profile likelihood estimation using the readily available R package mgcv, leading to straightforward computation. Simulation studies are considered under various link functions. In addition, we examine different choices of smoothing parameters. Simulation results and real data applications show effectiveness of the proposed approach. Finally, some large sample properties are established.

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UC Authors

Yan Yu
Yan Yu