Local linear estimate of the point at high risk: Spatial functional data case

Abeidallah, M.; Mechab, Boubaker; Merouan, Torkia

doi:10.1080/03610926.2019.1580735

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…where η i are independent and identically distributed and follow the normal distribution N (0, 0.2), while the random variables b i are generated from a uniformly distributed on the interval [1,3] (b i ∼ U ([1, 3])). All the curves X i 's are generated from 100 equidistant values in [0, 1] 6.1.…”

Section: Simulationmentioning

confidence: 99%

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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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Section: Simulationmentioning

confidence: 99%

“…On the other hand, the local linear estimation of the point at high risk in the case where observations are spatially dependent. We can cite Abeidallah et al [1]. For more results on the local linear approach ( see, for instance, Benhenni et al [5], Al-Awadhi et al [1], Attouch et al [2] and Chahad et al [10]).…”

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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show abstract

“…B-splines only require a few (the degree of the polynomial plus two) basis functions and are easy to implement [17][18][19]. Another method is local linear fit [20][21][22], but the difficulty is in choosing the bandwidth, especially when the observation points are uneven. Therefore, in this paper we employ reproducing kernel Hilbert space (RKHS), a special form of spline method in which the turning point from curve estimation to point estimation Yuan and Cai [12] explored its application on functional linear regression problem, and Lei and Zhang [23] extented it to RKHS-based partially functional linear models.…”

Section: Introductionmentioning

confidence: 99%

Representation Theorem and Functional CLT for RKHS-Based Function-on-Function Regressions

Huang

et al. 2022

Mathematics

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We investigate a nonparametric, varying coefficient regression approach for modeling and estimating the regression effects caused by two functionally correlated datasets. Due to modern biomedical technology to measure multiple patient features during a time interval or intermittently at several discrete time points to review underlying biological mechanisms, statistical models that do not properly incorporate interventions and their dynamic responses may lead to biased estimates of the intervention effects. We propose a shared parameter change point function-on-function regression model to evaluate the pre- and post-intervention time trends and develop a likelihood-based method for estimating the intervention effects and other parameters. We also propose new methods for estimating and hypothesis testing regression parameters for functional data via reproducing kernel Hilbert space. The estimators of regression parameters are closed-form without computation of the inverse of a large matrix, and hence are less computationally demanding and more applicable. By establishing a representation theorem and a functional central limit theorem, the asymptotic properties of the proposed estimators are obtained, and the corresponding hypothesis tests are proposed. Application and the statistical properties of our method are demonstrated through an immunotherapy clinical trial of advanced myeloma and simulation studies.

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Covariance estimation error of incomplete functional data under RKHS framework

Yao

2023

Applied Mathematics and Computation

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Local linear estimate of the point at high risk: Spatial functional data case

Cited by 4 publications

References 21 publications

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

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

Representation Theorem and Functional CLT for RKHS-Based Function-on-Function Regressions

Covariance estimation error of incomplete functional data under RKHS framework

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