Nonparametric Statistics for Stochastic Processes

Bosq, Denis

doi:10.1007/978-1-4684-0489-0

Cited by 297 publications

(153 citation statements)

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“…Exponential inequalities play important roles in stochastic processes; see Chapter 1 in Bosq (1996) for an extensive treatment, where applications to nonparametric inference are discussed. However, rigid strong mixing conditions are needed in the latter book, which may fail for many interesting applications.…”

Section: An Exponential Inequalitymentioning

confidence: 99%

Limit theorems for iterated random functions

Shao

2004

J. Appl. Probab.

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We study geometric-moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models.

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Section: An Exponential Inequalitymentioning

confidence: 99%

Limit theorems for iterated random functions

Shao

2004

J. Appl. Probab.

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“…In order to make this idea clear and to show the crucial helpfulness of the results of this work in many purposes, we look more closely at the interesting problem of functional estimation for continuous time processes (Priestley (1981), Bosq (1998)). Let X = {X t } t∈T be a real continuous-time stochastic process (T ⊂ R), which is strictly stationary and strongly mixing (see section 2).…”

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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“…We refer the reader to the books by Györfi et al (1989) and Bosq (1996) for surveys of the field of nonparametric time series prediction. We consider a typical result established in Györfi et al (1989) (see Section 3.4) for compactly supported φ-mixing processes.…”

Section: Structural Risk Minimization For Time Seriesmentioning

confidence: 99%

“…While many appealing mathematical properties of the parametric approach have been established, it has become clear over the years that the limitations of the approach are rather severe, in their imposition of a rigid structure on the process. One of the more productive solutions to this problem has been the extension of the classic nonparametric methods to the case of time series (see, for example, Györfi et al (1989) and Bosq (1996) for a review). In this work we use the term parametric model to refer to any model which imposes a specific form on the estimated function, which is exactly known up to a finite number of parameters.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Meir

2000

Machine Learning

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Abstract.We consider the problem of one-step ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. We make use of recent results from the theory of empirical processes, and adapt the uniform convergence framework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametric rates of convergence through an extension of the method of structural risk minimization suggested by Vapnik. All our results are derived for general L p error measures, and apply to both exponentially and algebraically mixing processes.

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Nonparametric Statistics for Stochastic Processes

Cited by 297 publications

References 0 publications

Limit theorems for iterated random functions

Limit theorems for iterated random functions

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

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