arXiv subjects

M. P. Frías

Publications and source records attributed to M. P. Frías.

5 recordsLinked to original sources

arXiv2025

Global Fréchet regression from time correlated bivariate curve data in manifolds

Global Fréchet 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 Fréchet 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 Fréchet functional mean. A weighted Fréchet mean approach is adopted in the definition of the theoretical loss function. The regularized Fréchet 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 Fréchet 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 Fréchet 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↗

arXiv2022

Point pattern analysis and classification on compact two-point homogeneous spaces evolving time

This paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold M_{d}, defined by a connected and compact two-point homogeneous space, including the special case of the sphere. The presented approach is based on temporal Cox processes driven by a L^{2}(\mathbb{M}_{d})-valued log-intensity. Different aggregation schemes on the manifold of the spatiotemporal point-referenced data are implemented in terms of the time-varying discrete Jacobi polynomial transform of the log-risk process. The n-dimensional microscale point pattern evolution in time at different manifold spatial scales is then characterized from such a transform. The simulation study undertaken illustrates the construction of spherical point process models displaying aggregation at low Legendre polynomial transform frequencies (large scale), while regularity is observed at high frequencies (small scale). K-function analysis supports these results under temporal short-, intermediate- and long-range dependence of the log-risk process.

stat.ME↗

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↗

arXiv2020

A spatial functional count model for heterogeneity analysis in time

A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive l2-valued processes (SARl2 processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality.

stat.ME↗