arXiv subjects

A. Torres-Signes

Publications and source records attributed to A. Torres-Signes.

4 recordsLinked to original sources

arXiv2025

Local Fr\'echet functional regression in manifolds from time-correlated bivariate curve data

Under mild conditions, a least-squares local linear Fr\'echet curve predictor is derived for a response and a regressor evaluated in a separable Hilbert space. The conditions that allow the implementation of the local linear Fr\'echet functional predictor in the ambient L2-space of vector functions, with values in the time-varying tangent space of a compact Riemannian manifold, are established. An intrinsic local linear Fr\'echet curve predictor on such a manifold is then proposed, based on a weighted Fr\'echet mean approach. Its asymptotic optimality is proved. Simulations and a real-data application are considered to analyze the finite-sample performance of the empirical versions of both predictors, compared with a geodesic Nadaraya-Watson-type curve predictor. In the real-data application, the functional prediction of the time-varying spherical coordinates of the Earth's magnetic field is addressed usingobservations through time of the geocentric latitude and longitude of the NASA MAGSAT spacecraft.

math.ST↗

arXiv2022

Global Fr\'echet regression from time correlated bivariate curve data in manifolds

Global Fr\'echet regression is addressed from the observation of a strictly stationary bivariate curve process, evaluated in a finite--dimensional compact differentiable Riemannian manifold, with bounded positive smooth sectional curvature. The involved univariate curve processes respectively define the functional response and regressor, having the same Fr\'echet functional mean. The supports of the marginal probability measures of the regressor and response processes are assumed to be contained in a ball, whose radius ensures the injectivity of the exponential map. This map has time--varying origin at the common marginal Fr\'echet functional mean. A weighted Fr\'echet mean approach is adopted in the definition of the theoretical loss function. The regularized Fr\'echet weights are computed, in the time--varying tangent space from the log--mapped regressors. Under these assumptions, and some Lipschitz regularity sample path conditions, when a unique minimizer exists, the uniform weak--consistency of the empirical Fr\'echet curve predictor is obtained, under mean--square ergodicity of the log--mapped regressor process in the first two moments. A simulated example in the sphere illustrates the finite sample size performance of the proposed Fr\'echet predictor. Predictions in time of the spherical coordinates of the magnetic field vector are obtained from the time--varying geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft in the real--data example analyzed.

math.ST↗

arXiv2021

COVID-19 mortality analysis from soft-data multivariate curve regression and machine learning

A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities, since March, 8, 2020 until May, 13, 2020. An empirical comparative study with Machine Learning (ML) regression, based on random k-fold cross-validation, and bootstrapping confidence interval and probability density estimation, is carried out. This empirical analysis also investigates the performance of ML regression models in a hard- and soft- data frameworks. The results could be extrapolated to other counts, countries, and posterior COVID-19 waves.

stat.ML↗

arXiv2021

Spatial Cox processes in an infinite-dimensional framework

We introduce a new class of spatial Cox processes driven by a Hilbert--valued random log--intensity. We adopt a parametric framework in the spectral domain, to estimate its spatial functional correlation structure. Specifically, we consider a spectral functional, based on the periodogram operator, inspired on Whittle estimation methodology. Strong-consistency of the parametric estimator is proved in the linear case. We illustrate this property in a simulation study under a Gaussian first order Spatial Autoregressive Hilbertian scenario for the log--intensity model. Our method is applied to the spatial functional prediction of respiratory disease mortality in the Spanish Iberian Peninsula, in the period 1980--2015.

stat.ME↗