NONPARAMETRIC REGRESSION ON FUNCTIONAL DATA: INFERENCE AND PRACTICAL ASPECTS

By Frédéric Ferraty, André Mas, Philippe Vieu. 2007

226 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1e6c003fe524c2eb09f2c02ac7769b2130ff0976

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Citations in the corpus

A survey of functional principal component analysis (2014, unknown): “2 ) L”
Shrinkage estimation and selection for multiple functional regression (2011, methodology): “This dataset has been previously used in functional nonparametric regression studies where the covariate is the spectra curve and the response is the percentage of fat content in the piece of meat (Ferraty and Vieu, 2002, 2006; Ferraty et al., 2007).”
Cross-validated estimations in the single-functional index model (2008, background): “Theorem 1 in 25 gives pointwise rates of convergence for <inline-graphic xmlns:xlink="http://www.”
Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation (2017, methodology): “We follow Ferraty et al. (2007) and implement both methods with the kernel function K ( u ) = 1 − u 2 and the L 2 ( R ) norm between the second derivatives of the spectra as a distance measure.”
The functional linear array model (2015, methodology): “A fundamentally different approach is pursued by Ferraty et al. (2005, 2007) who estimate scalar-on-function regression models nonparametrically using kernel methods, yielding predictions but no interpretable models.”
Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, methodology): “This example is the same as that used in Ferraty et al. (2007) to illustrate bootstrap bandwidth selection.”
Nonparametric time series prediction: A semi-functional partial linear modeling (2008, methodology): “Exact computation of these constants can be obtained by means of the same techniques used in Ferraty, Mas and Vieu [9], so the additional assumption 3 is turned into a more interpretable condition.”
Mean estimation with data missing at random for functional covariables (2013, background): “[23] and Delsol [24], but extension to the MAR problem and to the averaged estimates is still an open question.”
Convergence of functional k-nearest neighbor regression estimate with functional responses (2011, methodology): “For functional regression with scalar responses, uniform convergence was obtained in [12], asymptotic normality was shown in [8, 6] for the independent case and α-mixing case respectively, and [7] studied inferences using bootstrap.”
On the Validity of the Bootstrap in Non‐Parametric Functional Regression (2009, background): “Asymptotic normality has been established in Masry (2005), Delsol (2009) and Ferraty et al. (2007).”
Advances on asymptotic normality in non-parametric functional time series analysis (2009, background): “11 have given exact expressions of variance and expectation for kernel estimators, which led them to a central limit theorem with explicit constants in the independent case.”