Rates of strong consistencies of the regression function estimator for functional stationary ergodic data

Laïb, Naâmane; Louani, Djamal

doi:10.1016/j.jspi.2010.06.009

Cited by 45 publications

(65 citation statements)

References 13 publications

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“…The results follow by making use of Lemma 1 and Lemma 2 in Laïb and Louani (2011). Details of the proof may be found in Laïb and Louani (2010).…”

Section: Proof Of Lemmamentioning

confidence: 98%

“…In fact, since the kernel K and the function H are bounded, it follows easily in view of Lemma 2 (ii) in Laïb and Louani (2011) that…”

Section: Proof Of Lemmamentioning

confidence: 99%

“…Examples of classes fulfilling the condition (5) are given throughout the literature, see, for instance, Laïb and Louani (2011) and Vaart and Wellner (1996).…”

Section: Commentmentioning

confidence: 99%

“…Moreover, considering Lemma 2 in Laïb and Louani (2011) combined with the condition A4(i) imply that…”

Section: Proof Of Lemmamentioning

confidence: 99%

“…Furthermore, using Condition (A1), which supposes almost surely that f i,1 is bounded by a deterministic function b(x) and that ψ i,x (h K ) ≤ φ(h K ) as h K → 0, together with Lemma 2 in Laïb and Louani (2011), we have for n large enough…”

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confidence: 99%

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Rate of uniform consistency for a class of mode regression on functional stationary ergodic data

2016

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The aim of this paper is to study the asymptotic properties of a class of kernel conditional mode estimates whenever functional stationary ergodic data are considered. To be more precise on the matter, in the ergodic data setting, we consider a random elements (X, Z ) taking values in some semi-metric abstract space E × F. For a real function ϕ defined on the space F and x ∈ E, we consider the conditional mode of the real random variable ϕ(Z ) given the event "X = x". While estimating the conditional mode function, say θ ϕ (x), using the well-known kernel estimator, we establish the strong consistency with rate of this estimate uniformly over VapnikChervonenkis classes of functions ϕ. Notice that the ergodic setting offers a more general framework than the usual mixing structure. Two applications to energy data are provided to illustrate some examples of the proposed approach in time series forecasting framework. The first one consists in forecasting the daily peak of electricity demand in France (measured in Giga-Watt). 123M. Chaouch et al.short-term forecasting of the electrical energy (measured in Giga-Watt per Hour) that may be consumed over some time intervals that cover the peak demand.

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“…The results follow by making use of Lemma 1 and Lemma 2 in Laïb and Louani (2011). Details of the proof may be found in Laïb and Louani (2010).…”

Section: Proof Of Lemmamentioning

confidence: 98%

“…In fact, since the kernel K and the function H are bounded, it follows easily in view of Lemma 2 (ii) in Laïb and Louani (2011) that…”

Section: Proof Of Lemmamentioning

confidence: 99%

“…Examples of classes fulfilling the condition (5) are given throughout the literature, see, for instance, Laïb and Louani (2011) and Vaart and Wellner (1996).…”

Section: Commentmentioning

confidence: 99%

“…Moreover, considering Lemma 2 in Laïb and Louani (2011) combined with the condition A4(i) imply that…”

Section: Proof Of Lemmamentioning

confidence: 99%

mentioning

confidence: 99%

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Rate of uniform consistency for a class of mode regression on functional stationary ergodic data

2016

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Consistency results of the M‐regression function estimator for stationary continuous‐time and ergodic data

Mokhtari

Rouane

Rahmani

et al. 2022

Stat

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This paper is devoted to the study of asymptotic properties of the kernel estimator of the robust regression function for stationary continuous‐time and ergodic data. Such a dependence structure is an alternative to the strong mixing conditions usually assumed in functional time series analysis. More precisely, we consider the kernel type estimator of the robust regression function constructed from the stationary and continuous‐time ergodic data false(Xt,Ytfalse) for 0≤t≤T. Then, we establish the almost sure (with rate) pointwise convergence of this estimator. A simulation study was conducted in order to compare the performance of this method to the classical regression method.

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On asymptotic properties of functional conditional mode estimation with both stationary ergodic and responses MAR

Ling

Liu

Vieu

2017

Contributions to Statistics

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Rates of strong consistencies of the regression function estimator for functional stationary ergodic data

Cited by 45 publications

References 13 publications

Rate of uniform consistency for a class of mode regression on functional stationary ergodic data

Rate of uniform consistency for a class of mode regression on functional stationary ergodic data

Consistency results of the M‐regression function estimator for stationary continuous‐time and ergodic data

On asymptotic properties of functional conditional mode estimation with both stationary ergodic and responses MAR

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