On the Local Linear Modelization of the Conditional Distribution for Functional Data

Demongeot, Jacques; Laksaci, Ali; Rachdi, Mustapha; Rahmani, Saâdia

doi:10.1007/s13171-013-0050-z

Cited by 39 publications

(22 citation statements)

References 27 publications

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“…We point out that this estimator is a functional version of the LLE proposed by Fan et al [37]. Such a version has been introduced by [40][41][42][43][44].…”

Section: Functional Local Linear Regression (Fllr)mentioning

confidence: 99%

Soil Quality Analysis Using Modern Statistics and NIR Spectroscopy Procedure

Almanjahie¹,

Ahmad²,

Elmezouar³

et al. 2019

Pol. J. Environ. Stud.

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In this paper, we combine the recent development on mathematical statistics with modern chemistry in order to provide a new approach for soil quality analysis. Precisely, from modern chemistry we use near-infrared reflectance (NIR) spectroscopy procedure as a fast, accurate and inexpensive tool to evaluate chemical properties. Based on the collected data, the relationship between soil quality variables is modeled by using the functional statistics, which allows for analyzing a data as a curve or an image. The used predictor models are functional classical regression (FCR), functional local linear regression (FLLR), functional relative error regression (FRER) and functional robust regression (FRR). We prove that the performance of these models is closely linked to the homogeneity of the data. Considering the Abisko soil data, we show that FNR and FLLR are suitable for soil organic matter data, while for the Ergosterol concentration data the use of FRER and FRR are adequate. Furthermore, the proposed functional approach, permits us to avoid many drawbacks of the classical approach as principal component regression (P.C.R.).

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“…We point out that this estimator is a functional version of the LLE proposed by Fan et al [37]. Such a version has been introduced by [40][41][42][43][44].…”

Section: Functional Local Linear Regression (Fllr)mentioning

confidence: 99%

Soil Quality Analysis Using Modern Statistics and NIR Spectroscopy Procedure

Almanjahie¹,

Ahmad²,

Elmezouar³

et al. 2019

Pol. J. Environ. Stud.

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“…It is observed that the assumptions listed above are standard in the FDA context. In particular, hypotheses (H1) and (H6) are not unduly restrictive and are common in the setting of the functional local linear fitting (see Barrientos-Marina et al [2], and Demongeot et al [12] among others). Concerning the first part of (H1), the reader will find, in Ferraty and Vieu [19], a deep discussion concerning the links between this assumption, the semi-metric d, and the small ball concentration properties.…”

Section: Comments On the Assumptionsmentioning

confidence: 99%

“…And it should be noted that the last precursor work has been extended in many directions, including asymptotic properties (see Demongeot et al. [11,12] and Zhou and Lin [37]), nature of the variables (see Demongeot et al [14]), or the dependence type (see Demongeot et al. [10] and Laksaci et al [27]).…”

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confidence: 99%

Local linear conditional cumulative distribution function with mixing data

Bouanani

Rahmani

Ait-Hennani³

2019

Arab. J. Math.

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This paper investigates a conditional cumulative distribution of a scalar response given by a functional random variable with an α-mixing stationary sample using a local polynomial technique. The main purpose of this study is to establish asymptotic normality results under selected mixing conditions satisfied by many time-series analysis models in addition to the other appropriate conditions to confirm the planned prospects.Mathematics Subject Classification 62G05 · 62G08 · 62G20 · 62G07 · 62G30 · 62H12 Introduction and motivationsWith the evolution of the measuring instruments and the growth of research studies mainly since the publication of the pioneer paper of Ferraty and Vieu [19], functional data analysis (FDA) has attracted the attention of many works as in the recent monograph of Horváth and Kokoszka [23]. On the other hand, alternative conditional predictions of the classical regression have also gained a considerable interest in basically all the fields of statistics, especially for estimating conditional models using the kernel approach (or local constant) as investigated in the papers of Ferraty et al. [18], , or Ezzahrioui and Ould-Saïd [15].In numerous nonparametric statistic problems, the estimation of a conditional distribution function (CDF) constitutes a key aspect of inference. Accordingly, the present study employs a specific CDF model for constructing prediction intervals that can be involved in many applications such as the survival analysis and reliability. Interestingly, it is well known that the CDF has the advantage to completely characterize the conditional law of the considered random variables. The determination of the CDF allows, in fact, to obtain the conditional density and conditional hazard functions. Moreover, several prediction tools can also be implemented for the nonparametric statistics modeling, taking the example of conditional mode, median, or quantile. In addition, an extensive literature including various nonparametric approaches has taken place in the conditional estimation of independent samples and dependent observations in finite-and infinite-dimensional spaces (see, for instance, Berlinet et al. [3], Honda [22], and Ferraty and Vieu [17]). In many situations, the

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“…However, Barrientos et al [4] investigated the almost complete convergence (with rate) of the local linear estimator of the regression function for independent data. After that, this technique has been applied for the estimation of other conditional models ( see Demongeot et al [14] for the conditional density and Demongeot et al [15] for the conditional distribution). Recently, the local linear estimation of the conditional hazard function when the observations are independent was obtained by Massim et al [29]).…”

Section: Introductionmentioning

confidence: 99%

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Bouanani¹,

Guendouzi²,

Chemikh³

2020

Preprint

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In this work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

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On the Local Linear Modelization of the Conditional Distribution for Functional Data

Cited by 39 publications

References 27 publications

Soil Quality Analysis Using Modern Statistics and NIR Spectroscopy Procedure

Soil Quality Analysis Using Modern Statistics and NIR Spectroscopy Procedure

Local linear conditional cumulative distribution function with mixing data

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

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