Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution when the sample is considered as an $\alpha$-mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function ({\em cond-cdf}) is introduced. Af...

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Main Authors:	Amina Angelika Bouchentouf, Souad Mekkaoui, Abbes Rabhi
Format:	Article
Language:	English
Published:	BİSKA Bilisim Company 2015-03-01
Series:	New Trends in Mathematical Sciences
Subjects:	Conditional quantile conditional cumulative distribution derivatives of conditional cumulative distribution functional random variable kernel estimator nonparametric estimation semi-metric strong mixing processes.
Online Access:	http://www.ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=74

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spelling	doaj-630532c1b11a4b12865c06672b5007d32020-11-24T21:57:30ZengBİSKA Bilisim CompanyNew Trends in Mathematical Sciences2147-55202147-55202015-03-013218119874Strong uniform consistency rates of conditional quantiles for time series data in the single functional index modelAmina Angelika Bouchentouf0Souad Mekkaoui1Abbes Rabhi2Amina Angelika Bouchentouf3Souad Mekkaoui4Abbes Rabhi5University of Sidi Bel AbbesUniversity of TlemcenUniversity of Sidi Bel AbbesUniversity of Sidi Bel AbbesUniversity of TlemcenUniversity of Sidi Bel AbbesThe main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution when the sample is considered as an $\alpha$-mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function ({\em cond-cdf}) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated {\em cond-cdf}, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis. For that, the whole observed time series has to be split into a set of functional data, and the functional conditional quantile approach can be employed both in foreseeing and building confidence prediction bands.http://www.ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=74Conditional quantileconditional cumulative distributionderivatives of conditional cumulative distributionfunctional random variablekernel estimatornonparametric estimationsemi-metricstrong mixing processes.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi
spellingShingle	Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model New Trends in Mathematical Sciences Conditional quantile conditional cumulative distribution derivatives of conditional cumulative distribution functional random variable kernel estimator nonparametric estimation semi-metric strong mixing processes.
author_facet	Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi Amina Angelika Bouchentouf Souad Mekkaoui Abbes Rabhi
author_sort	Amina Angelika Bouchentouf
title	Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
title_short	Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
title_full	Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
title_fullStr	Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
title_full_unstemmed	Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
title_sort	strong uniform consistency rates of conditional quantiles for time series data in the single functional index model
publisher	BİSKA Bilisim Company
series	New Trends in Mathematical Sciences
issn	2147-5520 2147-5520
publishDate	2015-03-01
description	The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution when the sample is considered as an $\alpha$-mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function ({\em cond-cdf}) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated {\em cond-cdf}, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis. For that, the whole observed time series has to be split into a set of functional data, and the functional conditional quantile approach can be employed both in foreseeing and building confidence prediction bands.
topic	Conditional quantile conditional cumulative distribution derivatives of conditional cumulative distribution functional random variable kernel estimator nonparametric estimation semi-metric strong mixing processes.
url	http://www.ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=74
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Strong uniform consistency rates of conditional quantiles for time series data in the single functional index model

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