Model selection using wavelet decomposition and applications

Antoniadis, Anestis; Gijbels, Irène; Grègoire, Gèrard

doi:10.1093/biomet/84.4.751

Cited by 30 publications

(25 citation statements)

References 35 publications

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“…The initial OLS-ERR type algorithms, however, cannot automatically determine the model size. To ameliorate the agility and enhance the capability of the OLS-ERR algorithm, an approximate minimum description length (AMDL) criterion (Saito 1994, Antoniadis et al 1997, will be introduced to aid the determination of the associated model size, and this is described below.…”

Section: The Wavelet Modelmentioning

confidence: 99%

“…In the present study, an approximate minimum description length (AMDL) criterion developed by Saito (1994) and Antoniadis et al (1997), on the basis of the Rissanen's MDL criterion (Rissanen 1983), will be used to determine the model size. For the case of single regression model, AMDL is defined as…”

Section: Model Size Determinationmentioning

confidence: 99%

“…The dictionary may consist of a large number of candidate bases, but in many cases only a small number of significant bases need to be included in the wavelet model for a given nonlinear identification problem. An orthogonal least squares (OLS) algorithm interfered with by an error reduction ratio (ERR) index and regularised by an approximate minimum description length (AMDL) criterion (Saito 1994, Antoniadis et al 1997 , is used to select significant bases (model regressors). The performance of the resultant sparse wavelet models is compared with that of polynomial models, by inspecting the predictive capability of the associated representations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A comparative study on global wavelet and polynomial models for non-linear regime-switching systems

Wei

Billings

2007

IJMIC

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Abstract-A comparative study of wavelet and polynomial models for nonlinear regime-switching (RS) systems is carried out. Regime-switching systems, considered in this study, are a class of severely nonlinear systems, which exhibit abrupt changes or dramatic breaks in behavior, due to regime switching caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An orthogonal least squares (OLS) algorithm interfered with by an error reduction ratio (ERR) index and regularised by an approximate minimum description length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalization properties, for describing severely nonlinear regime-switching systems.Keywords-NARX models; Nonlinear system identification; Regime-switching systems; Wavelets. Abstract-A comparative study of wavelet and polynomial models for nonlinear regime-switching (RS) systems is carried out. Regime-switching systems, considered in this study, are a class of severely nonlinear systems, which exhibit abrupt changes or dramatic breaks in behavior, due to regime switching caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An orthogonal least squares (OLS) algorithm interfered with by an error reduction ratio (ERR) index and regularised by an approximate minimum description length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalization properties, for describing severely nonlinear regime-switching systems.

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Section: The Wavelet Modelmentioning

confidence: 99%

Section: Model Size Determinationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A comparative study on global wavelet and polynomial models for non-linear regime-switching systems

Wei

Billings

2007

IJMIC

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“…If we assume that τ is known their result applies to our model. For each J ∈ J , the Kullback risk for the maximum likelihood estimator of m when m = m J equals Q(J) defined at equation (4) and the likelihood penalised estimator is defined by J(pen) = arg min J∈J crit(J, pen), where…”

Section: Control Of the Quadratic Riskmentioning

confidence: 99%

Model selection for estimating the non zero components of a Gaussian vector

Huet¹

2006

ESAIM: PS

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“…The success of these applications can be attributed to the flexible nature of wavelet systems that allow them to adapt to the structure of the underlying process governing the behaviour of several systems. Several examples can be found in Abramovich & Silverman (1998), Härdle, Kerkyacharian, Picard & Tsybakov (1998), Antoniadis, Gijbels & Grégoire (1997) and Wang (1995). Herzberg & Traves (1994) were probably the first to discuss classical designs for wavelet regression models, in which the Haar wavelets are the regressors.…”

Section: Introductionmentioning

confidence: 99%

Minimax A‐ and D‐optimal integer‐valued wavelet designs for estimation

Oyet

2002

Can J Statistics

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Abstract:The author discusses integer-valued designs for wavelet estimation of nonparametric response curves in the possible presence of heteroscedastic noise using a modified wavelet version of the GasserMüller kernel estimator or weighted least squares estimation. The designs are constructed using a minimax treatment and the simulated annealing algorithm. The author presents designs for three case studies in experiments for investigating Gompertz's theory on mortality rates, nitrite utilization in bush beans and the impact of crash helmets in motorcycle accidents. Plans minimax A-et D-optimauxà valeurs entières pour l'estimation par ondelettesRésumé : L'auteur s'intéresse aux plansà valeurs entières facilitant, en présenceéventuelle de bruit hétéroscédastique, l'estimation par ondelettes de courbes de réponse non paramétriques au moyen d'un estimateur des moindres carrés pondérés ou d'une version modifiée pour ondelette de l'estimateurà noyau de Gasser-Müller. Les plans sont conçus au moyen d'un critère minimax et d'un algorithme de recuit simulé. L'auteur exploite ces plans dans trois cas de figure concernant la théorie de Gompertz sur les taux de mortalité, l'emploi de nitrite dans la fertilisation d'une variété de haricots et le comportement de casques de moto lors d'une collision.

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Model selection using wavelet decomposition and applications

Cited by 30 publications

References 35 publications

A comparative study on global wavelet and polynomial models for non-linear regime-switching systems

A comparative study on global wavelet and polynomial models for non-linear regime-switching systems

Model selection for estimating the non zero components of a Gaussian vector

Minimax A‐ and D‐optimal integer‐valued wavelet designs for estimation

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