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Structural test in regression on functional variables

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  • Delsol, Laurent
  • Ferraty, Frédéric
  • Vieu, Philippe

Abstract

Many papers deal with structural testing procedures in multivariate regression. More recently, various estimators have been proposed for regression models involving functional explanatory variables. Thanks to these new estimators, we propose a theoretical framework for structural testing procedures adapted to functional regression. The procedures introduced in this paper are innovative and make the link between former works on functional regression and others on structural testing procedures in multivariate regression. We prove asymptotic properties of the level and the power of our procedures under general assumptions that cover a large scope of possible applications: tests for no effect, linearity, dimension reduction, ...

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  • Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:422-447
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    4. Shang, Han Lin, 2016. "A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 95-104.
    5. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2013. "Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 421-444.
    6. Maistre, Samuel & Patilea, Valentin, 2020. "Testing for the significance of functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    7. Huang, Lele & Wang, Huiwen & Zheng, Andi, 2014. "The M-estimator for functional linear regression model," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 165-173.
    8. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    9. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.

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