
A robust spline approach in partially linear additive models
Partially linear additive models generalize the linear models since they...
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Robust FunctiononFunction Regression
Functional linear regression is a widely used approach to model function...
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Robust Regression via Mutivariate Regression Depth
This paper studies robust regression in the settings of Huber's ϵcontam...
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Mtype penalized splines for functional linear regression
Functional data analysis is a fast evolving branch of modern statistics,...
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Preliminary test estimation in ULAN models
Preliminary test estimation, which is a natural procedure when it is sus...
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Functional instrumental variable regression with an application to estimating the impact of immigration on native wages
Functional linear regression gets its popularity as a statistical tool t...
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Robust functional regression based on principal components
Functional data analysis is a fast evolving branch of modern statistics ...
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Robust estimation for semifunctional linear regression models
Semifunctional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a nonparametric component involving a univariate explanatory variable. It is of practical importance to obtain estimators for these models that are robust against highleverage outliers, which are generally difficult to identify and may cause serious damage to least squares and Hubertype Mestimators. For that reason, robust estimators for semifunctional linear regression models are constructed combining Bsplines to approximate both the functional regression parameter and the nonparametric component with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Consistency and rates of convergence for the proposed estimators are derived under mild regularity conditions. The reported numerical experiments show the advantage of the proposed methodology over the classical least squares and Hubertype Mestimators for finite samples. The analysis of real examples illustrate that the robust estimators provide better predictions for nonoutlying points than the classical ones, and that when potential outliers are removed from the training and test sets both methods behave very similarly.
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