On extended partially linear single-index models

Yingcun XIA, Howell TONG, Wai Keung LI

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79 Citations (Scopus)

Abstract

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
JournalBiometrika
Volume86
Issue number4
DOIs
Publication statusPublished - Dec 1999

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Single-index Model
Linear Model
Unknown
Nonlinear Time Series Analysis
Linear Approximation
Time series analysis
Random variable
Random variables
time series analysis
Model
Estimate
Index model
Nonlinear time series
Approximation

Citation

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

Keywords

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