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Distance-based local linear regression for functional predictors

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  • Boj, Eva
  • Delicado, Pedro
  • Fortiana, Josep

Abstract

The problem of nonparametrically predicting a scalar response variable from a functional predictor is considered. A sample of pairs (functional predictor and response) is observed. When predicting the response for a new functional predictor value, a semi-metric is used to compute the distances between the new and the previously observed functional predictors. Then each pair in the original sample is weighted according to a decreasing function of these distances. A Weighted (Linear) Distance-Based Regression is fitted, where the weights are as above and the distances are given by a possibly different semi-metric. This approach can be extended to nonparametric predictions from other kinds of explanatory variables (e.g., data of mixed type) in a natural way.

Suggested Citation

  • Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:429-437
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    References listed on IDEAS

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    Cited by:

    1. Zhiyong Zhou & Zhengyan Lin, 2016. "Asymptotic normality of locally modelled regression estimator for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 116-131, March.
    2. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    3. Chouaf Abdelhak & Laksaci Ali, 2012. "On the functional local linear estimate for spatial regression," Statistics & Risk Modeling, De Gruyter, vol. 29(3), pages 189-214, August.
    4. Fatiha Messaci & Nahima Nemouchi & Idir Ouassou & Mustapha Rachdi, 2015. "Local polynomial modelling of the conditional quantile for functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 597-622, November.
    5. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    6. Bouabsa Wahiba, 2023. "The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(1), pages 17-32, March.
    7. Oussama Bouanani & Saâdia Rahmani & Ali Laksaci & Mustapha Rachdi, 2020. "Asymptotic normality of conditional mode estimation for functional dependent data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 465-481, June.
    8. Abderrahmane Belguerna & Hamza Daoudi & Khadidja Abdelhak & Boubaker Mechab & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2024. "A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios," Mathematics, MDPI, vol. 12(3), pages 1-20, February.
    9. Aurea Grané & Alpha A. Sow-Barry, 2021. "Visualizing Profiles of Large Datasets of Weighted and Mixed Data," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    10. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    11. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    12. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    13. Raffaella Piccarreta, 2012. "Graphical and Smoothing Techniques for Sequence Analysis," Sociological Methods & Research, , vol. 41(2), pages 362-380, May.
    14. 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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