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Semi-functional partial linear quantile regression

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  • Ding, Hui
  • Lu, Zhiping
  • Zhang, Jian
  • Zhang, Riquan

Abstract

Semi-functional partial linear model is a flexible model in which a scalar response is related to both functional covariate and scalar covariates. We propose a quantile estimation of this model as an alternative to the least square approach. We also extend the proposed method to kNN quantile method. Under some regular conditions, we establish the asymptotic normality of quantile estimators of regression coefficient. We also derive the rates of convergence of nonparametric function. Finite-sample performance of our estimation is compared with least square approach via a Monte Carlo simulation study. The simulation results indicate that our method is much more robust than the least square method. A real data example about spectrometric data is used to illustrate that our model and approach are promising.

Suggested Citation

  • Ding, Hui & Lu, Zhiping & Zhang, Jian & Zhang, Riquan, 2018. "Semi-functional partial linear quantile regression," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 92-101.
    • Handle: RePEc:eee:stapro:v:142:y:2018:i:c:p:92-101
    DOI: 10.1016/j.spl.2018.07.007
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    References listed on IDEAS

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    1. Kehui Chen & Hans‐Georg Müller, 2012. "Conditional quantile analysis when covariates are functions, with application to growth data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 67-89, January.
    2. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    3. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    4. Germán Aneiros-Pérez & Philippe Vieu, 2011. "Automatic estimation procedure in partial linear model with functional data," Statistical Papers, Springer, vol. 52(4), pages 751-771, November.
    5. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
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    Cited by:

    1. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).

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