The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data

Mohammedi, Mustapha; Bouzebda, Salim; Laksaci, Ali

doi:10.1016/j.jmva.2020.104673

Cited by 27 publications

(8 citation statements)

References 53 publications

(72 reference statements)

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“…with ρ p (Y − s) is the scoring function, the p ∈ [0, 1] is called the asymmetry parameter level and I A represents the event's indicator function. The model ( 4) has been introduced in functional statistics by [18] (rep. [25]). Its functional estimation is given as follow…”

Section: Kfqe (Resp Kfee)mentioning

confidence: 99%

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

Almanjahie¹,

Fetitah²,

Attouch³

et al. 2023

Computers, Materials &Amp; Continua

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Functional statistics is a new technique for dealing with data that can be viewed as curves or images. Parallel to this approach, the Near-Infrared Reflectance (NIR) spectroscopy methodology has been used in modern chemistry as a rapid, low-cost, and exact means of assessing an object's chemical properties. In this research, we investigate the quality of corn and cookie dough by analyzing the spectroscopic technique using certain cutting-edge statistical models. By analyzing spectral data and applying functional models to it, we could predict the chemical components of corn and cookie dough.

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Section: Kfqe (Resp Kfee)mentioning

confidence: 99%

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

Almanjahie¹,

Fetitah²,

Attouch³

et al. 2023

Computers, Materials &Amp; Continua

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show abstract

“…Thus, the statistical modeling of these data as random functions resulted in a number of difficult theoretical and numerical research concerns; we may refer to [1][2][3][4][5][6] for parametric and nonparametric models. For the latest contributions in FDA and its related topics, one can refer to [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data

Litimein

Fatimah

Bouzebda

et al. 2023

Entropy

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The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is a fundamental tool in characterizing the convergence rate of the local linear estimation. Precisely, we use this tool to derive the uniform convergence rate of the local linear estimation of the conditional cumulative distribution function and the local linear estimation conditional quantile function. Second, a central limit theorem for the proposed estimators is established. These results are proved under general assumptions, allowing for the incomplete functional time series case to be covered. Specifically, we model the correlation using the ergodic assumption and assume that the response variable is collected with missing at random. Finally, we conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimators.

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“…This method frequently employs the [21] concept of expectiles, the least squares equivalent of the conventional quantiles. They were given this name because they resemble the quantiles of a random variable, but, unlike quantiles, they are based on a quadratic loss function, as in the case of the expectation; see [22][23][24][25] for more information. The expectile regression function has various uses in insurance, finance, and economics.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation

Laksaci,

Bouzebda,

Alshahrani

et al. 2023

Symmetry

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The problem of estimating the spatio-functional expectile regression for a given spatial mixing structure Xi,Yi∈F×R, when i∈ZN,N≥1 and F is a metric space, is investigated. We have proposed the M-estimation procedure to construct the Spatial Local Linear (SLL) estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the SLL expectile regression estimator. Precisely, we establish the almost-complete convergence with rate. This result is proven under some mild conditions on the model in the mixing framework. The implementation of the SLL estimator is evaluated using an empirical investigation. A COVID-19 data application is performed, allowing this work to highlight the substantial superiority of the SLL-expectile over SLL-quantile in risk exploration.

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The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data

Cited by 27 publications

References 53 publications

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

Functional Nonparametric Predictions in Food Industry Using Near-Infrared Spectroscopy Measurement

Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data

Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation

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