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M. D. Ruiz-Medina

Publications and source records attributed to M. D. Ruiz-Medina.

At least 19 recordsLinked to original sources
arXiv2026

Local Fréchet functional regression in manifolds from time-correlated bivariate curve data

Under mild conditions, a least-squares local linear Fréchet 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 Fréchet 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 Fréchet curve predictor on such a manifold is then proposed, based on a weighted Fréchet 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↗
arXiv2026

Long range dependence spectral testing from discretely observed functional time series in manifolds

A specification test for long range dependence (LRD) in functional time series in manifolds has been formulated in \cite{Ruiz-MedinaCrujeiras24} in the spectral domain for fully observed functional data. The asymptotic Gaussian distribution of the proposed test statistics, based on the weighted periodogram operator, under the null hypothesis, and the consistency of the test have been derived. In this paper, we analyze the asymptotic properties of this LRD spectral testing procedure, when the functional data are contaminated, and discretely observed through random uniform spatial sampling.

math.ST↗
arXiv2026

Testing the goodness-of-fit of a functional autoregressive model

The proposed Goodness--of--Fit (GoF) test for checking the linear autocorrelation model in a functional time series is based on an empirical process, whose residual marks and covariate index set are in a separable Hilbert space \mathbb{H}. A functional central limit theorem is derived providing the convergence of the empirical process to a time-changed Wiener process evaluated in a separable Hilbert space \mathbb{H}, with subordinator given by the marginal probability of the involved strictly stationary Autoregressive Hilbertian process (AR\mathbb{H}(1) process). The large sample behavior of the test statistics is obtained under simple and composite null hypotheses. The consistency of the test is addressed under simple null hypothesis. The finite-sample performance of the testing procedure, under different families of alternatives, and random projection schemes, is illustrated in the Appendix.

math.ST↗
arXiv2026

Noncentral limit results for spatiotemporal random fields on manifolds and beyond

This paper derives noncentral limit theorems (NCLTs) for suitable scaling of functionals of spatially homogeneous and isotropic, and stationary in time, LRD Gaussian subordinated Spatiotemporal Random Fields (STRFs) with Hermite rank equal to two. The cases of connected and compact two point homogeneous spaces \mathbb{M}_{d}\subset \mathbb{R}^{d+1}, and compact convex sets \mathcal{K}\subset \mathbb{R}^{d+1}, whose interior has positive Lebesgue measure, are analyzed. These NCLTs are obtained in the second Wiener Chaos by applying reduction theorems. The methodological approaches adopted in the derivation of these results are based on the pure point and continuous spectra of the Gaussian STRFs subordinators defined on \mathbb{M}_{d} and $\mathcal{K}, respectively.

math.PR↗
arXiv2025

Testing LRD in the spectral domain for functional time series in manifolds

A statistical hypothesis test for long range dependence (LRD) is formulated in the spectral domain for functional time series in manifolds. The elements of the spectral density operator family are assumed to be invariant with respect to the group of isometries of the manifold. The proposed test statistic is based on the weighted periodogram operator. A Central Limit Theorem is derived to obtain the asymptotic Gaussian distribution of the proposed test statistic operator under the null hypothesis. The rate of convergence to zero, in the Hilbert--Schmidt operator norm, of the bias of the integrated empirical second and fourth order cumulant spectral density operators is obtained under the alternative hypothesis. The consistency of the test follows from the consistency of the integrated weighted periodogram operator under LRD. Practical implementation of our testing approach is based on the random projection methodology. A simulation study illustrates, in the context of spherical functional time series, the asymptotic normality of the test statistic under the null hypothesis, and its consistency under the alternative. The empirical size and power properties are also computed for different functional sample sizes, and under different scenarios.

math.ST↗
arXiv2025

High-level moving excursions for spatiotemporal Gaussian random fields with long range dependence

The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal long-range dependence (LRD) Gaussian random fields are considered in this analysis. The limit results derived provide general reduction principles under increasing domain asymptotics in space and time. The case of time-varying thresholds is also studied. Thus, the family of morphological measures considered allows the statistical and geometrical analysis of random physical systems displaying structural changes over time. Motivated by cosmological applications, the derived results are applied to the context of sojourn measures of spatiotemporal spherical Gaussian random fields. The results are illustrated for some families of spatiotemporal Gaussian random fields displaying complex spatiotemporal dependence structures.

math.PR↗
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

Macroscale structural complexity analysis of subordinated spatiotemporal random fields

Large-scale behavior of a wide class of spatial and spatiotemporal processes is characterized in terms of informational measures. Specifically, subordinated random fields defined by non-linear transformations on the family of homogeneous and isotropic Lancaster-Sarmanov random fields are studied under long-range dependence (LRD) assumptions. In the spatial case, it is shown that Shannon mutual information beween marginal distributions for infinitely increasing distance, which can be properly interpreted as a measure of macroscale structural complexity and diversity, has an asymptotic power decay that directly depends on the underlying LRD parameter, scaled by the subordinating function rank. Sensitivity with respect to distortion induced by the deformation parameter under the generalized form given by divergence-based Rényi mutual information is also analyzed. In the spatiotemporal framework, a spatial infinite-dimensional random field approach is adopted. The study of the large-scale asymptotic behavior is then extended under the proposal of a functional formulation of the Lancaster-Sarmanov random field class, as well as of divergence-based mutual information. Results are illustrated, in the context of geometrical analysis of sample paths, considering some scenarios based on Gaussian and Chi-Square subordinated spatial and spatio-temporal random fields.

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↗
arXiv2022

Sojourn functionals for spatiotemporal random fields with long-memory

This paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time also known as long memory. Specifically, reduction theorems are derived for local functionals of nonlinear transformation of such fields, with Hermite rank m larger than or equal to 1, under general covariance structures. These results are proven to hold, in particular, for a family of non--separable covariance structures belonging to Gneiting class. For m=2, under separability of the spatiotemporal covariance function in space and time, the properly normalized Minkowski functional, involving the modulus of a Gaussian random field, converges in distribution to the Rosenblatt type limiting distribution for a suitable range of the long memory parameter.

math.PR↗
arXiv2021

Bayesian surface regression versus spatial spectral nonparametric curve regression

COVID-19 incidence is analyzed at the provinces of some Spanish Communities during the period February-October, 2020. Two infinite-dimensional regression approaches are tested. The first one is implemented in the regression framework introduced in Ruiz-Medina, Miranda and Espejo (2019). Specifically, a bayesian framework is adopted in the estimation of the pure point spectrum of the temporal autocorrelation operator, characterizing the second-order structure of a surface sequence. The second approach is formulated in the context of spatial curve regression. A nonparametric estimator of the spectral density operator, based on the spatial periodogram operator, is computed to approximate the spatial correlation between curves. Dimension reduction is achieved by projection onto the empirical eigenvectors of the long-run spatial covariance operator. Cross-validation procedures are implemented to test the performance of the two functional regression approaches.

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↗
arXiv2018

A note on strong-consistency of componentwise ARH(1) predictors

New results on strong-consistency, in the Hilbert-Schmidt and trace operator norms, are obtained, in the parameter estimation of an autoregressive Hilbertian process of order one (ARH(1) process). In particular, a strongly-consistent diagonal componentwise estimator of the autocorrelation operator is derived, based on its empirical singular value decomposition.

math.ST↗
arXiv2018

Strongly consistent autoregressive predictors in abstract Banach spaces

This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the componentwise estimator of the autocorrelation operator in the norm of the space $\mathcal{L}(B)$ of bounded linear operators on B. The strong consistency of the associated plug-in predictor then follows in the $B$-norm. A Gelfand triple is defined through the Hilbert space constructed in Kuelbs' Lemma \cite{Kuelbs70}. A Hilbert--Schmidt embedding introduces the Reproducing Kernel Hilbert space (RKHS), generated by the autocovariance operator, into the Hilbert space conforming the Rigged Hilbert space structure. This paper extends the work of \cite{Bosq00} and \cite{LabbasMourid02}.

math.ST↗
arXiv2018

The effect of the spatial domain in FANOVA models with ARH(1) error term

Functional Analysis of Variance (FANOVA) from Hilbert-valued correlated data with spatial rectangular or circular supports is analyzed, when Dirichlet conditions are assumed on the boundary. Specifically, a Hilbert-valued fixed effect model with error term defined from an Autoregressive Hilbertian process of order one (ARH(1) process) is considered, extending the formulation given in Ruiz-Medina (2016). A new statistical test is also derived to contrast the significance of the functional fixed effect parameters. The Dirichlet conditions established at the boundary affect the dependence range of the correlated error term. While the rate of convergence to zero of the eigenvalues of the covariance kernels, characterizing the Gaussian functional error components, directly affects the stability of the generalized least-squares parameter estimation problem. A simulation study and a real-data application related to fMRI analysis are undertaken to illustrate the performance of the parameter estimator and statistical test derived.

stat.AP↗