Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional <i>U</i>-statistics involving functional data

Bouzebda, Salim; Nemouchi, Boutheina

doi:10.1080/10485252.2020.1759597

Cited by 36 publications

(16 citation statements)

References 81 publications

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“…Many methods have been established and developed to construct, in asymptotically optimal ways, bandwidth selection rules for nonparametric kernel estimators especially for Nadaraya-Watson regression estimator we quote among them [32], [34], [47], [22], [13] and [14]. This parameter has to be selected suitably, either in the standard finite dimensional case, or in the infinite dimensional framework for insuring good practical performances.…”

Section: The Bandwidth Selection Criterionmentioning

confidence: 99%

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Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data

Souddi¹,

Madani²,

Bouzebda³

2021

Bulletin of the Inst. of Math. Academia Sinica(N.S.)

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The purpose of this paper is to establish the invariance principle for the conditional set-indexed empirical process formed by functional ergodic random variables. The limit theorems, discussed in this paper, are key tools for many further developments in functional data analysis involving empirical process techniques. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model.

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Section: The Bandwidth Selection Criterionmentioning

confidence: 99%

“…However, there are a few results for the empirical process considered functional framework, we may refer for recent references to [14,15,16], [9]. [19] obtained several very useful results for set-indexed conditional empirical processes in functional setting the strong mixing dependence.…”

Section: Introductionmentioning

confidence: 99%

Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data

Souddi¹,

Madani²,

Bouzebda³

2021

Bulletin of the Inst. of Math. Academia Sinica(N.S.)

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“…The main result regarding to generalization bounds in this setting is manifested in next section, the proof of this result relies on the techniques of U -statistics and its applications which can be found in Fuchs et al [22], Bouzebda and Nemouchi [23], Fuglsby et al [24], Privault and Serafin [25], Bachmann and Reitzner [26], and Garg and Dewan [27], and we skip the details here.…”

Section: B Multi-dividing Ontology Algorithm By Maximizing Auc Measurementioning

confidence: 99%

Theoretical Perspective of Multi-Dividing Ontology Learning Trick in Two-Sample Setting

Zhu

Hua

2020

IEEE Access

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The multi-dividing ontology learning framework has been proven to have a higher efficiency for tree-structured ontology learning, and in this work, we consider a special setting of this learning framework in which ontology sample set for each rate is divided into two groups. This setting can be regarded as the classic two-sample learning problem associated with multi-dividing ontology framework. In this work, we mainly focus on the theoretical analysis of multi-dividing two-sample ontology learning algorithm, whose ontology objective function is proposed, and the generalization bounds in this setting is obtained in terms of U-statistics technique. The theoretical result given is of potential guiding significance in the field of ontology engineering applications. INDEX TERMS small ontology, multi-dividing ontology learning, similarity measure I. INTRODUCE OF ONTOLOGY

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“…The work in [5] focuses on analyzing variance for functional data, whereas that in [6] is more concerned with regression analysis for Gaussian processes. Recent studies and surveys on functional data modeling and analysis can be found in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

2022

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The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values.

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Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data

Cited by 36 publications

References 81 publications

Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data

Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data

Theoretical Perspective of Multi-Dividing Ontology Learning Trick in Two-Sample Setting

Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

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