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Separation of linear and index covariates in partially linear single-index models

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  • Lian, Heng
  • Liang, Hua

Abstract

Motivated to automatically partition predictors into a linear part and a nonlinear part in partially linear single-index models (PLSIM), we consider the estimation of a partially linear single-index model where the linear part and the nonlinear part involves the same set of covariates. We use two penalties to identify the nonzero components of the linear and index vectors, which automatically separates covariates into the linear and nonlinear part, and thus solves the difficult problem of model structure identification in PLSIM. We propose an estimation procedure and establish its asymptotic properties, which takes into account constraints that guarantee identifiability of the model. Both simulated and real data are used to illustrate the estimation procedure.

Suggested Citation

  • Lian, Heng & Liang, Hua, 2016. "Separation of linear and index covariates in partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 56-70.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:56-70
    DOI: 10.1016/j.jmva.2015.08.017
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    Cited by:

    1. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    2. Jun Zhang & Junpeng Zhu & Zhenghui Feng, 2019. "Estimation and hypothesis test for single-index multiplicative models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 242-268, March.
    3. Jun Zhang & Xia Cui & Heng Peng, 2020. "Estimation and hypothesis test for partial linear single-index multiplicative models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 699-740, June.
    4. Hyung Park & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2021. "A constrained single‐index regression for estimating interactions between a treatment and covariates," Biometrics, The International Biometric Society, vol. 77(2), pages 506-518, June.
    5. Heng Lian, 2020. "Asymptotics of the Non‐parametric Function for B‐splines‐based Estimation in Partially Linear Models," International Statistical Review, International Statistical Institute, vol. 88(1), pages 142-154, April.

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