A Novel Estimation Method in Generalized Single Index Models
提出一种新的广义单指标模型估计方法，先用局部线性平滑得到回归函数的一致估计，再估计参数部分，解决了离散响应变量中稀疏和误设导致的收敛问题，并通过模拟和P2P借贷数据验证。
The single index and generalized single index models have been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables in the low-dimensional case. In this article, we propose a new estimation approach for generalized single index models E(Y | θ⊤X)=ψ(g(θ⊤X)) with ψ(·) known but g(·) unknown. Specifically, we first obtain a consistent estimator of the regression function by using a local linear smoother, and then estimate the parametric components by treating ψ(ĝ(θ⊤Xi)) as our continuous response. The resulting estimators of θ are asymptotically normal. The proposed procedure can substantially overcome convergence problems encountered in generalized linear models with discrete response variables when sparseness occurs and misspecification. We conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze a financial dataset from a peer-to-peer lending platform of China as an illustration.