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.
CitationXia, 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
- Kernel smoothing
- Nonlinear time series
- Partially linear model
- Single-index model