On extended partially linear single-index models

Yingcun XIA, Howell TONG, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

93 Citations (Scopus)


Aiming to explore the relation between the response y and the stochastic explanatory vector variable X beyond the linear approximation, we consider the single-index model, which is a well-known approach in multidimensional cases. Specifically, we extend the partially linear single-index model to take the form y=βT0X + φ(θT0X) + ε, where ε is a random variable with Εε=0 and var(ε)=σ2, unknown, β0 and θ0 are unknown parametric vectors and φ(.) is an unknown real function. The model is also applicable to nonlinear time series analysis. In this paper, we propose a procedure to estimate the model and prove some related asymptotic results. Both simulated and real data are used to illustrate the results. Copyright © 1999 Biometrika Trust.
Original languageEnglish
Pages (from-to)831-842
Issue number4
Publication statusPublished - Dec 1999


Xia, Y., Tong, H., & Li, W. K. (1999). On extended partially linear single-index models. Biometrika, 86(4), 831-842. doi: 10.1093/biomet/86.4.831


  • Alpha-mixing
  • Kernel smoothing
  • Nonlinear time series
  • Partially linear model
  • Single-index model


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