Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series

Ezzahrioui, M'hamed; Ould-Saı̈d, Elias

doi:10.1080/03610920802001870

Cited by 43 publications

(27 citation statements)

References 28 publications

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“…As a direct consequence of the Lemma 3, the result (26) (see Ezzahrioui and Ould-Saïd, 2010) and the expression (25), permit us to obtain the asymptotic normality for the conditional hazard estimator.…”

Section: Theorem 4 Under Conditions (H1)-(h11) We Havementioning

confidence: 99%

Nonparametric estimation of the maximum of conditional hazard function under dependence conditions for functional data

Rabhi¹,

Hammou²,

Djebbouri³

2015

jas

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Abstract. The maximum of the conditional hazard function is a parameter of great importance in statistics, in particular in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates based on convolution kernel techniques of the first derivative of the conditional hazard function, we establish the asymptotic behavior of a hazard rate in the presence of a functional explanatory variable and asymptotic normality of the maximum value in the case of a strong mixing process.Résumé. Le maximum ou encore le pointà haut risque d'une fonction de risque conditionnel est un paramètre d'un grand intérêt en statistique, notamment dans l'analyse de risque séismique, car il constitue le risque maximal de survenance d'un tremblement de terre dans un intervalle de temps donné. Au moyen d'estimations non paramétriques basés sur les techniques de noyau de convolution de la première dérivée de la fonction de hasard conditionnel, nousétablissons le comportement asymptotique d'un taux de hasard d'une variable explicative fonctionnelle ainsi que la normalité asymptotique de la valeur maximale pour un processus mélangeant.

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Section: Theorem 4 Under Conditions (H1)-(h11) We Havementioning

confidence: 99%

Nonparametric estimation of the maximum of conditional hazard function under dependence conditions for functional data

Rabhi¹,

Hammou²,

Djebbouri³

2015

jas

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“…For that we need to estimate the unknown parameters (plug-in method). We consider the consistent estimators Ferraty et al, 2006) and φ x (h)a j (x) (see (3.3) and Ezzahrioui and Ould Saïd, 2008), respectively.…”

Section: Conditional Confidence Interval (Cci)mentioning

confidence: 99%

“…1 consistency and asymptotic normality of the kernel estimator of the CQ were obtained in Ferraty et al (2005) and Ezzahrioui and Ould Saïd (2008), for the dependent case.…”

Section: Introductionmentioning

confidence: 95%

Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

2011

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In this paper, we study an L 1 -norm kernel estimator of the conditional quantile (CQ) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. The almost complete (a.co.) consistency and the asymptotic normality of this estimate are obtained when the sample is an α-mixing sequence. We illustrate our methodology by applying the estimator to climatological data.

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“…For the above reasons, conditional quantiles are used in many areas of applied research and are frequently used in a regression setup, called quantile regression (see Koenker (2005) for recent developments of quantile regression). Some authors (Ferraty et al, 2005;Ezzahrioui and Ould-Saïd, 2008) have been interested into the conditional quantile estimation with a scalar response and functional covariate in the non-i.i.d. case.…”

Section: Introductionmentioning

confidence: 99%

Non parametric learning approach to estimate conditional quantiles in the dependent functional data case

Henchiri

2016

Communications in Statistics - Theory and Methods

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In this paper, we focus on conditional quantile estimation when the covariates take their values in a bounded subspace of the functional space L 2 (T ), of square integrable random functions defined on some compact set T . We use a nonparametric learning approach based on Support Vector Machines technique. The main goal is to establish a weak consistency of the Support Vector Machines estimator of conditional quantile under exponentially strongly mixing functional input sequences. Our main result (the estimator satisfies an oracle inequality) extends a previous result for independent and identically distributed sample. We apply this estimator in practice through a real dataset study.

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Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series

Cited by 43 publications

References 28 publications

Nonparametric estimation of the maximum of conditional hazard function under dependence conditions for functional data

Nonparametric estimation of the maximum of conditional hazard function under dependence conditions for functional data

Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

Non parametric learning approach to estimate conditional quantiles in the dependent functional data case

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