Erratum of: ‘Non-parametric models for functional data, with application in regression, time-series prediction and curve discrimination’

Ferraty, Frédéric; Vieu, Philippe

doi:10.1080/10485250801999453

Cited by 14 publications

(3 citation statements)

References 2 publications

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“…As noted in Ferraty and Vieu (2008), this assumption is trivially satisfied in standard non-parametric problems with vector-valued covariates, but this is not necessarily true for any general abstract semi-metric space. Thus it is necessary to assume that the compact subset can be written such that ( C. 1) holds.…”

Section: A1 Conditions and Assumptionsmentioning

confidence: 99%

Partially linear varying coefficient models stratified by a functional covariate

Maity

Huang

2012

Statistics & Probability Letters

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We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.

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Section: A1 Conditions and Assumptionsmentioning

confidence: 99%

Partially linear varying coefficient models stratified by a functional covariate

Maity

Huang

2012

Statistics & Probability Letters

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“…In addition, this condition is fulfilled in usual nonparametric problems when X = R p is endowed with the Euclidean metric on R p (because κ = p suffices). However, this topological characteristic does not hold for any abstract semi-metric space, as [89] explains. Before we can use the delta-sequences approach to estimate the value of the regression operator r (k) (•) in the model ( 5), we must first have the following definition.…”

Section: Preliminaries and Estimation Proceduresmentioning

confidence: 99%

“…Ref. [89], discussed the assumption (7). This condition holds trivially for any finite-dimensional Euclidean space and remains valid for projection-based metric spaces with infinite dimensions.…”

Section: Comments On the Assumptionsmentioning

confidence: 99%

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

2022

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U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.

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Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications

Attaoui

Ling

2015

Metrika

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Erratum of: ‘Non-parametric models for functional data, with application in regression, time-series prediction and curve discrimination’

Cited by 14 publications

References 2 publications

Partially linear varying coefficient models stratified by a functional covariate

Partially linear varying coefficient models stratified by a functional covariate

Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences

Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications

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