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Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density

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  • Han Lin Shang

Abstract

We investigate the issue of bandwidth estimation in a functional nonparametric regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013) ['Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density', Computational Statistics & Data Analysis , 67, 185-198], we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya-Watson estimator that admits mixed types of regressors. We derive a likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a functional nonparametric regression model with mixed types of regressors.

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  • 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.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:599-615
    DOI: 10.1080/10485252.2014.916806
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    2. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    3. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    4. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    5. Salim Bouzebda & Youssouf Souddi & Fethi Madani, 2024. "Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    6. Gardes, Laurent & Girard, Stéphane, 2016. "On the estimation of the functional Weibull tail-coefficient," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 29-45.
    7. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.
    8. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. Leonie Selk & Jan Gertheiss, 2023. "Nonparametric regression and classification with functional, categorical, and mixed covariates," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 519-543, June.
    10. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    11. 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.
    12. Mustapha Rachdi & Ali Laksaci & Noriah M. Al-Kandari, 2022. "Expectile regression for spatial functional data analysis (sFDA)," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 627-655, July.

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