arXiv subjects

M. Dolores Ruiz-Medina

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

7 recordsLinked to original sources

arXiv2025

Climate change analysis from LRD manifold functional regression

This work is motivated by the problem of predicting downward solar radiation flux spherical maps from the observation of atmospheric pressure at high cloud bottom. To this aim nonlinear functional regression is implemented under strong-correlated functional data. The link operator reflects the heat transfer in the atmosphere. A latent parametric linear functional regression model reduces uncertainty in the support of this operator. An additive long-memory manifold-supported functional time series error models persistence in time of random fluctuations observed in the response. Time is incorporated via the scalar covariates in the latent linear functional regression model. The functional regression parameters in this model are supported on a connected and compact two point homogeneous space. Its Generalized Least--Squares (GLS) parameter estimation is achieved. When the second-order structure of the functional error term is unknown, its minimum contrast estimation is obtained in the spectral domain. The performance of the theoretical and plug-in nonlinear functional regression predictors is illustrated in the simulation study undertaken in the sphere. The Supplementary Material provides a detailed empirical analysis in the one way ANOVA context. The real-data application extends the purely spatial statistical analysis of atmospheric pressure at high cloud bottom, and downward solar radiation flux in Alegria et al. (2021) to the spatiotemporal context.

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arXiv2024

Manifold functional multiple regression model with LRD error term

This paper considers the problem of manifold functional multiple regression with functional response, time--varying scalar regressors, and functional error term displaying Long Range Dependence (LRD) in time. Specifically, the error term is given by a manifold multifractionally integrated functional time series (see, e.g., Ovalle--Muñoz \& Ruiz--Medina, 2024)). The manifold is defined by a connected and compact two--point homogeneous space. The functional regression parameters have support in the manifold. The Generalized Least--Squares (GLS) estimator of the vector functional regression parameter is computed, and its asymptotic properties are analyzed under a totally specified and misspecified model scenario. A multiscale residual correlation analysis in the simulation study undertaken illustrates the empirical distributional properties of the errors at different spherical resolution levels.

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arXiv2024

Prediction of air pollutants PM10 by ARBX(1) processes

This work adopts a Banach-valued time series framework for component-wise estimation and prediction, from temporal correlated functional data, in presence of exogenous variables. The strong-consistency of the proposed functional estimator and associated plug-in predictor is formulated. The simulation study undertaken illustrates their large-sample size properties. Air pollutants PM10 curve forecasting, in the Haute-Normandie region (France), is addressed by implementation of the functional time series approach presented

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arXiv2023

LRD spectral analysis of multifractional functional time series on manifolds

This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert-Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved under a semiparametric functional spectral framework in the Gaussian context. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The performance of both estimation procedures is illustrated in the simulation study, in the context of multifractionally integrated spherical functional autoregressive-moving average (SPHARMA(p,q)) processes.

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arXiv2021

Spectral analysis of long range dependence functional time series

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario, a weak--consistent parametric estimator of the long--memory operator is then obtained by minimizing, in the norm of bounded linear operators, a divergence information functional loss.

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arXiv2018

Classical and bayesian componentwise predictors for non-compact correlated ARH(1) processes

A special class of standard Gaussian Autoregressive Hilbertian processes of order one (Gaussian ARH(1) processes), with bounded linear autocorrelation operator, which does not satisfy the usual Hilbert-Schmidt assumption, is considered. To compensate the slow decay of the diagonal coefficients of the autocorrelation operator, a faster decay velocity of the eigenvalues of the trace autocovariance operator of the innovation process is assumed. As usual, the eigenvectors of the autocovariance operator of the ARH(1) process are considered for projection, since, here, they are assumed to be known. Diagonal componentwise classical and bayesian estimation of the autocorrelation operator is studied for prediction. The asymptotic efficiency and equivalence of both estimators is proved, as well as of their associated componentwise ARH(1) plugin predictors. A simulation study is undertaken to illustrate the theoretical results derived.

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arXiv2018

Asymptotic properties of a componentwise ARH(1) plug-in predictor

This paper presents new results on prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) process framework) is adopted. A componentwise estimator of the autocorrelation operator is formulated, from the moment-based estimation of its diagonal coefficients, with respect to the orthogonal eigenvectors of the auto-covariance operator, which are assumed to be known. Mean-square convergence to the theoretical autocorrelation operator, in the space of Hilbert-Schmidt operators, is proved. Consistency then follows in that space. For the associated ARH(1) plug-in predictor, mean absolute convergence to the corresponding conditional expectation, in the considered Hilbert space, is obtained. Hence, consistency in that space also holds. A simulation study is undertaken to illustrate the finite-large sample behavior of the formulated componentwise estimator and predictor. The performance of the presented approach is compared with alternative approaches in the previous and current ARH(1) framework literature, including the case of unknown eigenvectors.

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