A Novel Estimation Method in Generalized Single Index Models

作者：Zhang, Dixin; Wang, Yulin; Liang, Hua^*

来源：JOURNAL OF BUSINESS & ECONOMIC STATISTICS, 2023, 41(2): 399-413.

DOI：10.1080/07350015.2022.2027777

• Empirical processes
• Logistic regression
• MAVE
• PLSiM
• Single index model
• Tail probability inequality

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 vertical bar theta X-T)=psi(g(theta X-T)) with psi(center dot) known but g(center dot) 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 psi((g) over cap(theta X-T(i))) as our continuous response. The resulting estimators of theta 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.

• 单位
  南京大学