An Efficient Computation Strategy for Generalized Single-Index Models and Their Variants by Integrating With GAM

Various generalizations of single-index models and associated estimation methods have been developed. However, implementing these developed methods requires much effort to program, case by case, due to the lack of a common and flexible vehicle to cover them. We suggest an efficient computation strategy for easily estimating parameters and nonparametric functions in generalized single-index models and generalized partially linear single-index models by integrating with well-developed algorithms and packages for estimating the generalized additive models (Wood; Hastie and Tibshirani, GAM). Such an integration makes estimation in these index-type models much easier, expedient, and flexible and brings a lot of convenience. We briefly introduce the principle and extensively examine numerical performance for various scenarios. Numerical experiments indicate that the proposed strategy works well with finite sample sizes and is especially flexible to model structures. Finally, we analyze two real-data examples as an illustration.