arXiv subjects

Manuel Oviedo de la Fuente

Publications and source records attributed to Manuel Oviedo de la Fuente.

4 recordsLinked to original sources

arXiv2024

Functional Regression Models with Functional Response: A New Approach and a Comparative Study

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive model. The latter methods have in common that the covariates and the response are represented in a basis and so, can only be applied when the response and the covariates belong to a Hilbert space, while the proposed method only uses the distances among data and thus can be applied to those situations where any of the covariates or the response is not Hilbert, typically normed or even metric spaces with a real vector structure. A comparison of these methods with other procedures readily available in R is preformed in a simulation study and in real datasets showing the results of the advantages of the nonlinear proposals and the small loss of efficiency when the simulation scenario is truly linear. The comparison is done in the Hilbert case as it is the only scenario where all the procedures can be compared. Finally, the supplementary material provides a visualization tool for checking the linearity of the relationship between a single covariate and the response, another real data example, and a link to a GitHub repository where the code and data are available.} %and an example considering that the response is not Hilbertian.

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arXiv2018

Variable selection in Functional Additive Regression Models

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model based on the use of distance correlation proposed by \cite{Szekely2007}. For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, ...) of each variable. The algorithm has shown quite promising results when applied to simulations and real data sets.

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arXiv2016

Predicting seasonal influenza transmission using Regression Models with Temporal Dependence

In this manuscript, we use meteorological information in Galicia (Spain) to propose a novel approach to predict the incidence of influenza. Our approach extends the GLS methods in the multivariate framework to functional regression models with dependent errors. A simulation study shows that the GLS estimators render better estimations of the parameters associated with the regression model and obtain extremely good results from the predictive point of view. Thus they improve the classical linear approach. It proposes an iterative version of the GLS estimator (called iGLS) that can help to model complicated dependence structures, uses the distance correlation measure $\mathcal{R}$ to select relevant information to predict influenza rate and applies the GLS procedure to the prediction of the influenza rate using readily available functional variables. These kinds of models are extremely useful to health managers in allocating resources in advance for an epidemic outbreak.

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arXiv2016

The DD$^G$-classifier in the functional setting

The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some issues still remain. This paper is devoted to extending the DD-classifier in the following ways: first, to surpass the limitation of the DD-classifier when more than two groups are involved. Second to apply regular classification methods (like $k$NN, linear or quadratic classifiers, recursive partitioning,...) to DD-plots to obtain useful insights through the diagnostics of these methods. And third, to integrate different sources of information (data depths or multivariate functional data) in a unified way in the classification procedure. Besides, as the DD-classifier trick is especially useful in the functional framework, an enhanced revision of several functional data depths is done in the paper. A simulation study and applications to some classical real datasets are also provided showing the power of the new proposal.

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