Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

Shang, Han Lin

doi:10.1016/j.csda.2013.05.006

Cited by 16 publications

(15 citation statements)

References 76 publications

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“…A local version, also optimal in an asymptotic way, is proposed by Benhenni et al (2007). More recently, Bayesian strategies have been studied (Shang, 2013(Shang, , 2014, but only for simulation purposes.…”

Section: G Chagny and A Rochementioning

confidence: 98%

Adaptive estimation in the functional nonparametric regression model

Chagny

Roche

2016

Journal of Multivariate Analysis

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In this paper, we consider nonparametric regression estimation when the predictor is a functional random variable (typically a curve) and the response is scalar. Starting from a classical collection of kernel estimates, the bias-variance decomposition of a pointwise risk is investigated to understand what can be expected at best from adaptive estimation. We propose a fully data-driven local bandwidth selection rule in the spirit of the Goldenshluger and Lepski method. The main result is a nonasymptotic risk bound which shows the optimality of our tuned estimator from the oracle point of view. Convergence rates are also derived for regression functions belonging to Hölder spaces and under various assumptions on the rate of decay of the small ball probability of the explanatory variable. A simulation study also illustrates the good practical performances of our estimator.

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Section: G Chagny and A Rochementioning

confidence: 98%

Adaptive estimation in the functional nonparametric regression model

Chagny

Roche

2016

Journal of Multivariate Analysis

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“…where t represents the function support range and 0 ≤ t 1 ≤ t 2 ≤ · · · ≤ t 100 ≤ π are equispaced points within the function support range, a i , b i , c i are independently drawn from a uniform distribution on [0, 1], and n represents the sample size. The functional form of (4) is taken from Ferraty et al (2010b) and Shang (2013Shang ( , 2014b. Figure 1 presents a replication of 100 simulated smooth curves, along with the first-order derivative of the curves approximated by B-splines.…”

Section: Simulation Of Smooth Curvesmentioning

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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“…Rachdi and Vieu () consider a functional cross‐validation method for bandwidth selection and prove its asymptotic optimality. Shang () and Zhang et al. () propose a Bayesian method for simultaneously selecting the bandwidth and the unknown error density and show that it attains greater estimation accuracy than functional cross‐validation.…”

Section: Non‐parametric Scalar‐on‐function Regressionmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

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149

109

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Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

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Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

Cited by 16 publications

References 76 publications

Adaptive estimation in the functional nonparametric regression model

Adaptive estimation in the functional nonparametric regression model

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

Methods for Scalar‐on‐Function Regression

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