Rate of uniform consistency for nonparametric estimates with functional variables

By Frédéric Ferraty, Ali Laksaci, Amel Tadj, Philippe Vieu. 2010

191 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eaa1279743e1d55b75ce8395586123d8abc85d7b

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Citations in the corpus

Functional data: local linear estimation of the conditional density and its application (2013, background): “Then, the uniform almost-complete convergence of some nonparametric conditional models is showed in 11 .”
Mean estimation with data missing at random for functional covariables (2013, background): “Statistics, 2013 Vol. 47, No. 4, 688–706, http://dx.doi.org/10.1080/02331888.2011.650172 Mean estimation with data missing at random for functional covariables Frédéric Ferratya, Mariela Suedb* and Philippe Vieua aInstitut de Mathématiques, Université Paul Sabatier, Toulouse, France; bFacultad de Ci”
Curse of dimensionality and related issues in nonparametric functional regression (2011, background): “[20, 23, 2, 22, 6, 3, 4, 7, 13] or [14] for a few paths in that direction.”
On the Local Linear Modelization of the Conditional Distribution for Functional Data (2014, background): “…section there are various alternative approaches permitting to select the smoothing parameters hH and hK (cf. for instance (Hall et al., 1999) for the linear model in the finite dimensional case and (Ferraty et al., 2010) for the regression estimation in the infinite dimensional framework).”
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.”
Kernel regression with functional response (2011, methodology): “In the special simpler case when Y is real this result was given in [4].”
Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “Precisely, under general conditions (see [22]), it can be shown that the uniform rates of convergence are alterated by the entropy function in the following way:”
Functional kernel estimators of large conditional quantiles (2011, background): “Its rate of uniform strong consistency is established by [16].”