Strong consistency with rates of spectral estimation of continuous-time processes: from periodic and poisson sampling schemes

Rachdi, Mustapha

doi:10.1080/10485250410001656426

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Concerning the association between stationary processes and point processes, the nearest work to our is the investigation done by Rolski (1984) to establish the ergodicity of the sampled process, and by Resnick and Samorodnitsky (2004) for α-stable processes, however, these works do not answer the questions posed here. The estimation of the spectral density function for continuous time process from sampling design was studied by Masry(1978), Lii and Masry (1994) and Rachdi (1999Rachdi ( , 2003Rachdi ( and 2004. The main goal of this paper is to study how to transmit the stationarity and the mixing properties from X to the sampled process X.…”

Section: Preprint Submitted To Elsevier Science 30 August 2007mentioning

confidence: 99%

On the statistical properties of a stationary process sampled by a stationary point process

Charlot¹,

Rachdi²

2008

Statistics & Probability Letters

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.On the statistical properties of a stationary process sampled by a stationary point processTo cite this version: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p tOn the statistical properties of a stationary process sampled by a stationary point process AbstractLet X = {X t } t∈T , where T = R or Z, be a strictly stationary process, which is assumed to be strongly mixing. In this paper, we are concerned with the stationarity and the mixing properties of the process obtained from X by a random sampling, that is, {X tn } n∈Z , where {t n } n∈Z is a real point process. This study is done for ϕ, β, ρ and α-mixing processes.

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Section: Preprint Submitted To Elsevier Science 30 August 2007mentioning

confidence: 99%

On the statistical properties of a stationary process sampled by a stationary point process

Charlot¹,

Rachdi²

2008

Statistics & Probability Letters

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“…• L'hypothèse (F1) est équivalente à l'existence de l'intégrale stochastique (1), l'hypothèse (F2) autorise à la fois des mbf, des processus à bande finie (voirRachdi, 2004), les processus localement fractionnaires utilisés par Kammoun et al (2007) pour modéliser les battements cardiaques ou des processus • n→∞ 0 est naturelle. Seule l'hypothèse d'indépendance des instants d'observations par rapport au processus est restrictive pour les applications en finance, mais elle est toujours faite, nous renvoyons sur ce point à Aït-Sahalia et Mykland (2008).…”

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Estimation non-paramétrique de la densité spectrale d'un processus gaussien échantillonné aléatoirement

Bardet,

Bertrand,

Billat

2008

Preprint

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En utilisant une analyse en ondelette, on construit un estimateur non-paramétrique de la densité spectrale d'un processus gaussien à accroissements stationnaires. Dans un premier temps, on considère le cas "idéal" de l'observation d'une trajectoire en temps continu et on donne un théorème de la limite central ponctuel et une estimation de l'erreur quadratique moyenne intégrée. Puis, afin de mieux correspondre aux applications, on construit un second estimateur à partir de l'observation d'une trajectoire du processus à des instants discrets, aléatoires et irrégulièrement espacés. Cet estimateur est obtenu en remplaçant les coefficients d'ondelette par leurs discrétisations. Nous donnons un second théorème de la limite central, avec une vitesse différente. Des simulations et une application à la modélisation du rythme cardiaque des marathoniens sont présentées.

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The effect of the regularity of the error process on the performance of kernel regression estimators

Benhenni

Rachdi

2012

Metrika

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International audienceThis article considers estimation of regression function f in the fixed design model Y(xi)=f(xi)+ϵ(xi),i=1,...,n , by use of the Gasser and Müller kernel estimator. The point set {xi}ni=1⊂[0,1] constitutes the sampling design points, and ϵ(xi) are correlated errors. The error process ϵ is assumed to satisfy certain regularity conditions, namely, it has exactly k ( =0,1,2,... ) quadratic mean derivatives (q.m.d.). The quality of the estimation is measured by the mean squared error (MSE). Here the asymptotic results of the mean squared error are established. We found that the optimal bandwidth depends on the (2k+1) th mixed partial derivatives of the autocovariance function along the diagonal of the unit square. Simulation results for the model of k th order integrated Brownian motion error are given in order to assess the effect of the regularity of this error process on the performance of the kernel estimator

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Strong consistency with rates of spectral estimation of continuous-time processes: from periodic and poisson sampling schemes

Cited by 3 publications

References 13 publications

On the statistical properties of a stationary process sampled by a stationary point process

On the statistical properties of a stationary process sampled by a stationary point process

Estimation non-paramétrique de la densité spectrale d'un processus gaussien échantillonné aléatoirement

The effect of the regularity of the error process on the performance of kernel regression estimators

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