Thresholding in Nonparametric Functional Regression with Scalar Response

Ferraty, Frédéric; Martínez-Calvo, Adela; Vieu, Philippe

doi:10.1007/978-3-7908-2736-1_16

Cited by 5 publications

(4 citation statements)

References 3 publications

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“…Up to our knowledge, its optimality (with respect to the mean integrated squared error for instance) is not established in the functional framework. We refer to [17] for such a work in functional regression.…”

Section: Illustration On Simulated Datamentioning

confidence: 99%

Functional kernel estimators of large conditional quantiles

Gardès¹,

Girard²

2012

Electron. J. Statist.

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International audienceWe address the estimation of conditional quantiles when the covariate is functional and when the order of the quantiles converges to one as the sample size increases. In a first time, we investigate to what extent these large conditional quantiles can still be estimated through a functional kernel estimator of the conditional survival function. Sufficient conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed estimators. In a second time, basing on these result, a functional Weissman estimator is derived, permitting to estimate large conditional quantiles of arbitrary large order. These results are illustrated on finite sample situations

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Section: Illustration On Simulated Datamentioning

confidence: 99%

Functional kernel estimators of large conditional quantiles

Gardès¹,

Girard²

2012

Electron. J. Statist.

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“…[26][27][28][29][30][31], among others. For scalar-on-function nonlinear regression models, the authors of [32] emphasized nonparametric techniques, particularly kernel-type estimation. Such tools were subsequently expanded to include discrimination and classification analysis.…”

Section: Introductionmentioning

confidence: 99%

Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data

Bouzebda,

Souddi,

Madani

2024

Mathematics

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This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic (1−α)-confidence interval is provided for 0<α<1 as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology.

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“…The functional estimate has been a topic of great interest in the statistical literature. To obtain a summary of the current state of non-parametric functional data, we refer to the work in [1,2]. The hazard function, also known as the risk function, is a concept commonly used in survival analysis and reliability theory.…”

Section: Introductionmentioning

confidence: 99%