Nonparametric local linear regression estimation for censored data and functional regressors

Leulmi, Sara

doi:10.1007/s42952-020-00080-7

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…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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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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Strong convergence of a nonparametric relative error regression estimator under missing data with functional predictors

Boucetta,

Guessoum,

Ould-Said

2024

J. Korean Stat. Soc.

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Local linear estimation of the trimmed regression for censored data

Bakhtaoui

Limam-Belarbi

2022

Filomat

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We introduce a non-parametric estimation of the trimmed regression by using the local linear method of a censored scalar response variable, given a functional covariate. The main result of this work is the establishment of almost complete convergence for the constructed estimator. A simulation study is carried out to compare the finite sample performance based on the mean square error between the classic local linear regression estimator and the trimmed local linear regression estimator. Moreover, a real data study is used to illustrate our methodology.

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Nonparametric local linear regression estimation for censored data and functional regressors

Cited by 4 publications

References 18 publications

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

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

Strong convergence of a nonparametric relative error regression estimator under missing data with functional predictors

Local linear estimation of the trimmed regression for censored data

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