Penalised spline estimation for generalised partially linear single-index models

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• 作者：Yan Yu ; Chaojiang Wu ; Yuankun Zhang
• 关键词：Generalised linear model ; Generalised additive model ; Low rank approximation ; Penalised splines ; Profile likelihood
• 刊名：Statistics and Computing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：27
• 期：2
• 页码：571-582
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science;
• 出版者：Springer US
• ISSN：1573-1375
• 卷排序：27

文摘

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.