Estimation of a functional single index model with dependent errors and unknown error density

Shang, Han Lin

doi:10.1080/03610918.2018.1535068

Cited by 4 publications

(1 citation statement)

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“…Further, Shang (2016) uses marginal likelihood as a means of selecting the optimal semi-metric. Building on the early work by , and Shang (2013Shang ( , 2014aShang ( ,b, 2016Shang ( , 2020, we consider a kernel error-density estimator which explores data-driven features, such as asymmetry, skewness, and multi-modality, and relies on residuals obtained from the estimated regression function and bandwidth of residuals. Differing from those early work, we derive an approximate likelihood and a posterior for the functional partial linear model (a semiparametric model).…”

Section: Introductionmentioning

confidence: 99%

Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

Shang

2020

Journal of Applied Statistics

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This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.

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Section: Introductionmentioning

confidence: 99%

Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

Shang

2020

Journal of Applied Statistics

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A link function specification test in the single functional index model

Chan

Delsol

Goia

2023

Adv Data Anal Classif

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In this paper a test for specification in functional regression with scalar response that exploits semi-parametric principles is illustrated. Once the test statistics is defined, its asymptotic null distribution is derived under suitable conditions. The finite sample performances of the test are analyzed through a simulation study by using both the asymptotic p-value and some bootstrap approaches. To appreciate the potentialities of the method, an application to a spectrometric real dataset is performed.

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