Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes

Bosq, Denis

doi:10.1007/978-94-011-3222-0_38

Cited by 85 publications

(82 citation statements)

References 4 publications

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“…For additional case-studies or theoretical developments see, e.g., Boente and Fraiman (2000), Bosq (1991), Brumback and Rice (1998), Dauxois, Pousse and Romain (1982), Fan and Lin (1998), Ferraty and Vieu (1999), Hastie and Mallows (1993), Kneip (1994), Kneip and Gasser (1992), Locantore et al (1999), Ramsay and Dalzell (1991), Rice and Silverman (1991) and references therein. This paper is concerned with the problem of regression with functional data.…”

Section: Linear Functional Regression: Some Backgroundmentioning

confidence: 99%

Linear functional regression: The case of fixed design and functional response

2002

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Acknowledgements: We are very grateful to Kazaros Kazarian for some useful conversations. The useful and constructive comments of three referees are gratefully acknowledged. This work has been partially supported by DGESIC Spanish Grants PB97-0021 (A. Cuevas) and PB98-0182-C02-02, PGIDT99MA 20701 (M. Febrero). The problem of simple linear regression, with functional explanatory variables and functional response, is considered under a fixed design model. An estimator for the underlying linear operator is proposed. Its consistency is proved under some conditions which ensure that the design is informative enough. The classical calibration (or "inverse regression") problem is considered and a consistent estimator is analyzed. A simulation study is also given. The proposed method is computationally feasible and is not hard to implement in practice.

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Section: Linear Functional Regression: Some Backgroundmentioning

confidence: 99%

Linear functional regression: The case of fixed design and functional response

2002

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“…In addition to the wavelet packet basis approach, two methods presented by Bosq (1991) and Antoniadis & Sapatinas (2003) are used in the simulation. First method suggest the projection of the covariance operator on the span of principal components.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Then an estimation will have the form as in equation (4). Under certain assumptions on the covariance operator, this estimator is consistent(for details see ([Bosq (1991)])). For less regular space Antoniadis & Sapatinas (2003) proposed the method based on the wavelet-vaguelette decomposition and which is defined as follows…”

Section: Simulation Resultsmentioning

confidence: 99%

Estimation of the autoregressive operator by wavelet packets

Laukaitis¹,

Vasilecas²,

Laukaitis³

2009

Statistics & Probability Letters

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In this paper, we suggest to use wavelet packet bases as an alternative to the widely used principal component analysis in an estimation of the functional autoregressive processes. By extending the notion of the socalled nonstandard form of operators representation, we search for the "best" basis on a criterion of highest correlation between pairs of wavelet packet coefficients.KEY WORDS:autoregressive Hilbertian process, functional data analysis, wavelet packet bases,ill-posed inverse problem.

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“…The simulations of θ 0 (t) = sin(4πt) are of particular interest, as we are able to compare the estimates produced by the method presented in this paper and the results given by Cardot et al (1999Cardot et al ( , 2003, who derived an estimator for θ 0 through a method introduced by Bosq (1991Bosq ( , 2000 in the case of ARH processes.…”

Section: Examplesmentioning

confidence: 96%

Least Squares Consistent Estimates for Arbitrary Regression Functions Over an Abstract Space

Fiorin¹,

Parpinel²

2012

Communications in Statistics - Theory and Methods

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In this article, we propose a new approach to sieve estimation for a general regression function when the dimension of the finite dimensional subspaces is a random quantity depending on the values of the observations. The technique is introduced with the help of a simulation study on a functional linear model under extremely mild assumptions. A sketch of the proof concerning the main statements is then given in the more general case when the regression function is not necessarily linear

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Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes

Abstract: AIlS C1 ••• .i.f.i.cat.i.on and autor.qr ••• .i.v. proc ••• , proc ••• , m.i.x.i.nq. Key Worda B.i.1b.rt 509 62M Pr.d.i.ct.i.on, .pac., cont.i.nuou. t.i.m.

Cited by 85 publications

References 4 publications

Linear functional regression: The case of fixed design and functional response

Linear functional regression: The case of fixed design and functional response

Estimation of the autoregressive operator by wavelet packets

Least Squares Consistent Estimates for Arbitrary Regression Functions Over an Abstract Space

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