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Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

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  • Han Shang
Abstract
In the context of semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:829-848
    DOI: 10.1007/s00180-013-0463-0
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    3. 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.
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    5. Boente, Graciela & Salibian-Barrera, Matías & Vena, Pablo, 2020. "Robust estimation for semi-functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    6. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    7. Fanrong Zhao & Baoxue Zhang, 2024. "A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model," Mathematics, MDPI, vol. 12(16), pages 1-24, August.
    8. Shuyu Meng & Zhensheng Huang, 2024. "Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    9. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.

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