Testing Linearity in Functional Partially Linear Models

Zhao, Fanrong; Zhang, Baoxue

doi:10.1007/s10255-023-1040-0

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…More recently, [12] studied different bootstrapping procedures for this model under dependency structures. Additionally, a procedure for testing linearity in partially linear functional models is proposed in [13]. Other approaches have been proposed to estimate SPFLR model parameters; we cite, for example, the local linear approach used by [14], the robust procedures considered by [15], the k nearest neighbors (kNN) procedure used by [16] and Bayesian approaches proposed by [17].…”

Section: Of 21mentioning

confidence: 99%

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

Benchikh,

Almanjahie,

Fetitah

et al. 2023

Preprint

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The aim of this paper is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random. The estimators are constructed by the kernel method, and some asymptotic properties such as probability convergence rates of the nonparametric component and asymptotic distribution of the parametric and nonparametric components are established under certain conditions. Next, the performances and the superiority of these estimators are presented and examined using a study on simulated data and on real data by carrying out a comparison between our semi-functional partially linear model with MAR estimator (SFPLRM), the semi-functional partially linear model with the full-case estimator (SFPLRC) and the nonparametric functional model estimator with MAR (FNPM). The results show that the proposed estimators outperform existing estimators as the number of random missing data increases.

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Section: Of 21mentioning

confidence: 99%

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

Benchikh,

Almanjahie,

Fetitah

et al. 2023

Preprint

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“…More recently, Aneiros-Pérez et al [5] studied different bootstrapping procedures for this model under dependency structures while Ling et al [31] considers SPFLR models with random missing responses. A procedure for testing linearity in partially linear functional models is proposed in [39] while the extension of this model for spatial data was proposed by [13].Other approaches have been proposed to estimate SPFLR model parameters, we cite for example, the local linear approach (LLE) used by [22], the robust procedures considered by [15], the k nearest neighbors (kNN) procedure used by [30] and Bayesian approaches proposed by [37]. For the most recent contributions in this area, we can consult the bibliographic reviews in [33,34].…”

Section: Introductionmentioning

confidence: 99%

Local linear-$k$NN smoothing for semi-functional partial linear regression

Nassima Houda,

Tawfik,

Amina

et al. 2024

Hacettepe Journal of Mathematics and Statistics

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The aim of this paper is to study a semi-functional partial linear regression model. The estimators are constructed by k-nearest neighbors local linear method. Some asymptotic results are established for an i.i.d sample under certain conditions, including asymptotic normality of the parametric component and the almost certain convergence (with rate) of the non-parametric component. Lastly, using cross-validation, the performances of our estimation method are presented on simulated data and on real data by comparing them with other known approaches for semi-functional partial linear regression models.

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A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model

Zhao,

Zhang

2024

Mathematics

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The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data.

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Testing Linearity in Functional Partially Linear Models

Cited by 3 publications

References 26 publications

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

Nonparametric Partial Linear Estimation for Spatial Functional Data with Missing At-Random

Local linear-$k$NN smoothing for semi-functional partial linear regression

A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model

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