Robust estimation for semi-functional linear regression models

Boente, Graciela; Salibián‐Barrera, Matías; Vena, Pablo

doi:10.1016/j.csda.2020.107041

Cited by 15 publications

(11 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following Lemma gives conditions under which C8 holds. Its proof follows the same arguments as those considered in Boente et al (2020b).…”

Section: Proof Of Proposition 34 Recall Thatmentioning

confidence: 78%

See 1 more Smart Citation

A robust spline approach in partially linear additive models

Boente¹,

Martínez²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Partially linear additive models generalize the linear models since they model the relation between a response variable and covariates by assuming that some covariates are supposed to have a linear relation with the response but each of the others enter with unknown univariate smooth functions. The harmful effect of outliers either in the residuals or in the covariates involved in the linear component has been described in the situation of partially linear models, that is, when only one nonparametric component is involved in the model. When dealing with additive components, the problem of providing reliable estimators when atypical data arise, is of practical importance motivating the need of robust procedures. Hence, we propose a family of robust estimators for partially linear additive models by combining B−splines with robust linear regression estimators. We obtain consistency results, rates of convergence and asymptotic normality for the linear components, under mild assumptions. A Monte Carlo study is carried out to compare the performance of the robust proposal with its classical counterpart under different models and contamination schemes. The numerical experiments show the advantage of the proposed methodology for finite samples. We also illustrate the usefulness of the proposed approach on a real data set.

show abstract

“…The following Lemma gives conditions under which C8 holds. Its proof follows the same arguments as those considered in Boente et al (2020b).…”

Section: Proof Of Proposition 34 Recall Thatmentioning

confidence: 78%

“…. , g p , ς) with probability one, uniformly over a ∈ R, ς > 0, b ∈ R q and S 1 × • • • × S p and its proof uses similar arguments to those considered in the proof of Lemma S.1.2 in Boente et al (2020b). We include it for the sake of completeness.…”

Section: Final Commentsmentioning

confidence: 99%

A robust spline approach in partially linear additive models

Boente¹,

Martínez²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This method is called S-estimation because it depends on the estimation of the scale of errors [4]. The method of least squares was generalized by (Rousseeuw & Yahai) [6] to provide this new category of estimation in the framework of (Sestimation) and this method reduces the total errors to the lowest possible and is very resistant to anomalies found in data […”

Section: S-estimationmentioning

confidence: 99%

Comparing Some of Robust the Non-Parametric Methods for Semi-Parametric Regression Models Estimation

Kh.Bahez¹,

Rasheed²

2022

JEAS

View full text Add to dashboard Cite

In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing. The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the (M-LLS) method was the best, while the second model showed in general that the S-LLS method was the best in addition to the method M-LLS was the best in some cases of sample sizes and at different levels of variance. As for the third model, it was shown through the results that in most cases the S-LLS method was the best in addition to the M-LLS method which was better in some cases of sample sizes and at different levels of variance.

show abstract

“… Spatial: The spatial variability is considered in many research articles such as The partial functional linear spatial regression autoregressive model with spatial dependence responses [38], with two-stage estimator based on quasi-maximum likelihood estimation (QMLE) method and local linear regression method [39], studying the asymptotic normality of the parametric component, and probability convergence with the rate of the nonparametric component [40], B-spline approximation for slope function and residualbased approach for pointwise confidence-intervals [41], the robust spatial autoregressive model with t-distribution error terms with an expectationmaximization algorithm [42].  Robust: Existing outliers in the data or violations from distributional assumptions yield to the robust methods such as the sieve M-estimator for semi-functional linear model [43], with polynomial splines to approximate the slope parameter and resistance to heavy-tailed errors or outliers in the response [44], different estimators such as M-estimators with bi-square function, GM-estimator with Huber function, LMS-estimator and LTS-estimators [45], estimation based on exponential squared loss and FPCA [46], estimation based on the class of scale mixtures of normal (SMN) distributions for measurement errors and Bayesian framework with MCMC algorithm [47], Robust MM-estimators with B-Spline approximation [48], with modal regression [49] and a modified Huber's function with tail function with a data-driven procedure for selecting the tuning parameters [50].  Testing: Different hypothesis and testing statistics are developed ,such as: testing the linear component [51,52] with B-spline [53], functional covariates [54], densely and sparsely observed single and multiple functional covariates with four tests such as Wald, Score, likelihood ratio and F [55], Goodness-of-fit tests with wild bootstrap resampling, false discovery rate and independence test with generalized distance covariance or new metric, functional martingale difference divergence (FMDD), [56][57][58], series correlation test [59].…”

Section: Other Extensionsmentioning

confidence: 99%

A Literature Review of Semi-functional Partial Linear Regression Models

Fayaz¹

2021

Preprint

View full text Add to dashboard Cite

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

show abstract

Robust estimation for semi-functional linear regression models

Cited by 15 publications

References 56 publications

A robust spline approach in partially linear additive models

A robust spline approach in partially linear additive models

Comparing Some of Robust the Non-Parametric Methods for Semi-Parametric Regression Models Estimation

A Literature Review of Semi-functional Partial Linear Regression Models

Contact Info

Product

Resources

About