# María Dolores Ruiz-MedinaUniversity of Granada | UGR · Department Statistics and Operations Research

María Dolores Ruiz-Medina

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163

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Introduction

**Skills and Expertise**

## Publications

Publications (163)

The presented methodology for testing the goodness-of-fit of an Autoregressive Hilbertian model (ARH(1) model) provides an infinite-dimensional formulation of the approach proposed in Koul and Stute (1999), based on empirical process marked by residuals. Applying a central and functional central limit result for Hilbert-valued martingale difference...

This paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold Md,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb...

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 $m\geq 1,$ under general covariance structu...

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...

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 aggre...

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 L2 (M_d)– valued log–intensity. Different aggregation scheme...

Fr\'echet global regression is extended to the context of bivariate curve stochastic processes with values in a Riemannian manifold. The proposed regression predictor arises as a reformulation of the standard least-squares parametric linear predictor in terms of a weighted Fr\'echet functional mean. Specifically, in our context, in this reformulati...

COVID–19 incidence is analyzed at the provinces of the Spanish Communities in the Iberian Peninsula during the period February–October, 2020. Two infinite–dimensional regression approaches, surface regression and spatial curve regression, are proposed. In the first one, Bayesian maximum a posteriori (MAP) estimation is adopted in the approximation...

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 estimatio...

Sojourn measures have played a crucial role in the description of geometric characteristics of random surfaces, providing information on level crossing and possible extreme values. An extensive literature can be found in the field of stochastic processes, and statistics. Particularly, the asymptotic behavior, when the window size grows, of the volu...

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 diver...

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 diver...

This paper presents a multivariate functional data statistical approach, for spatiotemporal prediction of COVID-19 mortality counts. Specifically, spatial heterogeneous nonlinear parametric functional regression trend model fitting is first implemented. Classical and Bayesian infinite-dimensional log-Gaussian linear residual correlation analysis is...

This paper presents a multivariate functional data statistical approach , for spatiotemporal prediction of COVID-19 mortality counts. Specifically, spatial heterogeneous nonlinear parametric functional regression trend model fitting is first implemented. Classical and Bayesian infinite-dimensional log-Gaussian linear residual correlation analysis i...

A new class of spatial Cox processes, driven by a spatial infinite-dimensional random intensity, is introduced. Spatial curve prediction techniques can then be applied to approximate this double stochastic counting process family. A parametric framework is adopted for the spatial functional estimation of the correlation structure in the spectral do...

This paper contributes with some asymptotic results to the spectral analysis of functional time series. Specifically, the convergence to zero, in the Hilbert-Schmidt operator norm, of the functional bias associated with the periodogram operator is obtained. The uniform convergence to zero of its eigenvalues then follows. The convergence to zero of...

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...

The restriction to the sphere of a homogeneous and isotropic random field defines a spherical isotropic random field. This paper derives central and noncentral limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in R ³ . Both scenarios are motiva...

A new class of spatial log-Gaussian Cox processes in function spaces is introduced under suitable conditions. Its least-squares spatial functional predictor is formulated. The special case where the log-intensity is a Gaussian first-order spatial autoregressive Hilbertian process is analysed, and its minimum-contrast componentwise parameter estimat...

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

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a comp...

This paper presents a new result on strong-consistency, in the trace norm, of a diagonal componentwise parameter estimator of the autocorrelation operator of an autoregressive process of order one (ARH(1) process), allowing strong-consistency of the associated plug-in predictor. These results are derived, when the eigenvectors of the autocovariance...

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 d...

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a comp...

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 component-wise estimator of the autocorrelation operator in the norm of the space L(B) of bounded linear operators on B. The strong consistency of the associ...

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 L(B) of bounded linear operators on B. The strong consistency of
the associa...

This paper introduces new results on doubly stochastic Poisson processes, with log-Gaussian Hilbert-valued random intensity (LGHRI), defined from the Ornstein–Uhlenbeck process (O-U process) in Hilbert spaces. Sufficient conditions are derived for the existence of a counting measure on ℓ² for this type of doubly stochastic Poisson processes. Functi...

This work derives new results on the strong-consistency of a componentwise estimator of the autocorrelation operator, and its associated plug-in predictor, in the context of autoregressive processes of order one, in a real separable Banach space $B$ (ARB(1) processes). For the estimator of the autocorrelation operator, strong-consistency is proved,...

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...

This paper extends to the Banach-valued framework previous strong-consistency results derived, in the context of diagonal componentwise estimation of the autocorrelation operator of autoregressive Hilbertian processes, and the associated plug-in prediction. The Banach space B considered here is \( B = {\fancyscript{C}}\left( {\left[ {0,1} \right]}...

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 velocit...

Spatial-depth functional regression is applied for the estimation of ocean temperature, with projection onto the eigenvectors of the empirical covariance operator of the functional response (i.e., onto the Empirical Orthogonal Functions in space and depth). Moment-based estimation is performed to approximate the regression operators in the subspace...

In this paper we present novel results on the asymptotic behavior of the so-called Ibragimov minimum contrast estimates. The case of tapered data for various models of Gaussian random fields is investigated. The CLT for quadratic forms with tapered data is presented. © 2017, Institute of Mathematical Statistics. All rights reserved.

In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates
are analyzed by simulation experiments. By numerical simulation, we prove that consistency and asymptotic normality of the least-squares parameter estimator studied
holds under di...

This paper presents new results on the prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) framework) is adopted. A component-wise estimator of the autocorrelation operator is derived from the moment-based estimation of its diagonal coefficients with respect to the orthogonal eigen...

This paper derives the weak-sense Gaussian solution to a family of fractional-in-time and multifractional-in-space stochastic partial differential equations, driven by fractional-integrated-in-time spatiotemporal white noise. Some fundamental results on the theory of pseudodifferential operators of variable order, and on the Mittag-Leffler function...

This paper addresses the problem of spatial prediction from strong spatial correlated high-dimensional data. Two approaches are considered: spatial wavelet kernel penalized nonparametric regression, and wavelet shrinkage. The best performance corresponds to spatial wavelet thresholding techniques applied to coarser scales, when slowly varying data...

New results on functional prediction of the Ornstein-Uhlenbeck process in an autoregressive Hilbert-valued and Banach-valued frameworks are derived. Specifically, consistency of the maximum likelihood estimator of the autocorrelation operator, and of the associated plug-in predictor is obtained in both frameworks. https://doi.org/10.1016/j.spl.2016...

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the definition of a weak-sense Gaussian solution, in the mean-square sense, are derived. The temporal, spatial and spatio...

This paper introduces new results on doubly stochastic Poisson processes, with log-Gaussian Hilbert-valued random intensity (LGHRI), defined from the Ornstein-Uhlenbeck process (O-U process) in Hilbert spaces. Sufficient conditions are derived for the existence of a counting measure on l2, for this type of doubly stochastic Poisson processes. Funct...

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials.
The results on consistency and asymptotic normality of a class of minimum
contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for cons...

This paper studies the asymptotic properties of a plug-in predictor, based on the formulation of a componentwise estimator of the autocorrelation operator, for a special class of standard autoregressive Hilbertian processes of order one (ARH(1) processes). In the Gaussian case, double asymptotic functional plug-in prediction intervals are derived....

Potential theory and Dirichlet’s priciple constitute the basic elements of the well-known classical theory of Markov processes and Dirichlet forms. This paper presents new classes of fractional spatiotemporal covariance models, based on the theory of non-local Dirichlet forms, characterizing the fundamental solution, Green kernel, of Dirichlet boun...

A new wavelet-based estimation methodology, in the context of spatial functional regression, is proposed to discriminate between small-scale and large scale variability of spatially correlated functional data, defined by depth-dependent curves. Specifically, the discrete wavelet transform of the data is computed in space and depth to reduce dimensi...

This paper presents new results on Functional Analysis of Variance for fixed
effect models with correlated Hilbert-valued Gaussian error components. The
geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is
considered in the computation of the total sum of squares, the residual sum of
squares, and the sum of squares due to th...

In this paper, the estimation of parameters in the harmonic regression with
cyclically dependent errors is addressed. Asymptotic properties of the
least-squares estimates are analyzed by simulation experiments. By numerical
simulation, we prove that consistency and asymptotic normality of the
least-squares parameter estimator studied holds under di...

Fractional (in time and in space) evolution equations driven by fractional
integrated in time Gaussian spatiotemporal white noise are studied on Dirichlet
regular bounded open domains. A unique mean-square continuous solution is
derived. The mean-quadratic local variation properties of such a solution are
obtained from the asymptotic properties of...

A reduction theorem is proved for functionals of Gamma-correlated random
fields with long-range dependence in d-dimensional space. In the particular
case of a non-linear function of a chi-squared random field with Laguerre rank
equal to one, we apply the Karhunen-Lo\'eve expansion and the Fredholm
determinant formula to obtain the characteristic fu...

Local criteria based on validation data to select a predictor at each spatial location of a domain \(D\subset \mathbb {R}^{d}\) are proposed in a non-parametric setting. The resulting combination of spatial predictors is referred as locally selected predictor (LSP). Classical and more recently formulated spatial predictors can be considered as cand...

Problems related to weather forecast, forest attributes estimation and prediction, disease propagation, among others, are commonly approximated in the framework of multivariate Gaussian random field modeling. This paper deals with the equivalence condition of two zero-mean Gaussian infinite-dimensional vector measures defined on the finite product...

The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used
to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals
of quadratic functions of Gaussian stationary random fields on R^d displaying
long-range dependence. This distribution reduces to the usual Rosenblatt
distribution when d=1. Several properties...

This paper addresses, in a nonparametric functional statistical framework, the problem of classification of nonlinear features of curve and surface data in control systems. Specifically, on the one hand, in the detection of nonlinear dynamic features, wavelength absorbance curve data are analyzed for different meat pieces to discriminate between tw...

This paper proposes a spatial functional formulation of the normal mixed effect model for the statistical classification of spatially dependent Gaussian curves, in both parametric and state space model frameworks. Fixed effect parameters are represented in terms of a functional multiple regression model whose regression operators can change in spac...

This paper introduces spatial long-range dependence time series models, based on the consideration of fractional difference operators associated with Gegenbauer polynomials. Their structural properties are analyzed. The spatial autoregressive Gegenbauer case is also studied, including the case of k factors with multiple singularities. An extension...

Fractional-order pseudodifferential equations are considered to represent ocean climate variability when anomalous diffusion processes affect heat transfer in ocean surface. The driven process of these equations is assumed to be a regular spatiotemporal Gaussian random field representing normal conditions in the ocean. Linear regression in the log-...

Sufficient conditions are derived for the asymptotic efficiency and equivalence of componentwise Bayesian and classical estimators of the infinite-dimensional parameters characterizing l 2 valued Poisson process, and Hilbert valued Gaussian random variable models. Conjugate families are considered for the Poisson and Gaussian univariate likelihoods...

A minimum contrast criterion for consistently estimating the spatial fractal dimension in the wavelet domain is presented in [M. D. Ruiz-Medina and R. M. Crujeiras, Comm. Statist. Theory Methods., 40 (2011), pp. 3599–3613] for a class of semiparametric fractal Gaussian random fields, which includes fractional Brownian motion and Riesz-Bessel motion...

This paper derives conditions under which a stable solution to the least-squares linear estimation problem for multifractional random fields can be obtained. The observation model is defined in terms of a multifractional pseudodifferential equation. The weak-sense and strong-sense formulations of this problem are studied through the theory of fract...

This paper deals with the estimation of hidden periodicities in a non-linear
regression model with stationary noise displaying cyclical dependence.
Consistency and asymptotic normality are established for the least-squares
estimates.

This article addresses the problem of defining a general scaling setting in which Gaussian and non-Gaussian limit distributions of linear random fields can be obtained. The linear random fields considered are defined by the convolution of a Green kernel, satisfying suitable scaling conditions, with a non-linear transformation of a Gaussian centered...

This article introduces a Hilbert-valued spatially dynamic regression model. The spatially heterogeneous functional trend is modeled by functional multiple regression, with varying regression operators. The spatial autoregressive Hilbertian model of order one (SARH(1) model, see [3737.
Ruiz-Medina , M.D. 2011 . Spatial autoregressive and moving av...

In this article, the estimation of spatiotemporal long-range dependence is formulated in the spectral wavelet domain. Sample information is provided by functional spectral data. Their high local singularity at the origin is captured by the wavelet transform. Weak consistency of the spectral wavelet estimators proposed is derived. Two functional est...

Spatio–temporal statistical models have been proposed for the analysis of the temporal evolution of the geographical pattern of mortality (or incidence) risks in disease mapping. However, as far as we know, functional approaches based on Hilbert-valued processes have not been used so far in this area. In this paper, the autoregressive Hilbertian pr...

The autoregressive Hilbertian process framework has been introduced in Bosq (2000). This book provides the nonparametric estimation of the autocorrelation and covariance operators of the autoregressive Hilbertian processes. The asymptotic properties of these estimators are also provided. The maximum likelihood approach still remains unexplored. Thi...

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear f...

This chapter provides a general overview on the main results derived by the authors in relation to limit theory for the solution of linear and non-linear random evolution equations. Additionally, the local regularity properties of the solution to fractional pseudodifferential equations driven by random innovations are introduced. Specifically, limi...

In this article, we study the effect of the geometry of a domain with variable local dimension on the regularity/singularity of the restriction of a multifractional random field on such a domain. The theories of reproducing kernel Hilbert spaces (RKHS) and generalized random fields are applied. Fractional Sobolev spaces of variable order are consid...

A functional classification methodology, based on the Reproducing Kernel Hilbert Space (RKHS) theory, is proposed for discrimination of gene expression profiles. The parameter function involved in the definition of the functional logistic regression is univocally and consistently estimated, from the minimization of the penalized negative log-likeli...

Spatial Functional Statistics has emerged as a powerful tool in the spatial and spatiotemporal analysis of data arising, for example, from Agriculture, Geology, Soils, Hydrology, Environment, Ecology, Mining, Oceanography, Air Quality, Remote Sensing, Spatial Econometrics, Epidemiology, just to mention a few areas of application. However, big black...

This paper addresses the problem of spatial functional extrapolation in the framework of spatial autoregressive Hilbertian
processes of order one (SARH(1) processes) introduced in Ruiz-Medina (J Muitivar Anal 102:292–305, 2011a). Moment-based estimators of the operators involved in the state equation of these processes are computed by projection in...

This paper focuses on the problem of functional statistical classification of gene expression curves. A local-wavelet-vaguelette-based functional logistic regression approach is presented. This approach is specially suitable for the classification of non-stationary singular (non-differentiable) curves. The performance of the methodology proposed is...

Functional Statistics provides a suitable framework for the analysis of large dimensional data sets. In this paper, we consider the spatial autoregressive functional series (SARH(1)) framework. This framework allows the incorporation of spatial interaction to the statistical analysis of functional data (see Ruiz-Medina [1], [2]). The SARH(1) model...

For random fields with fractional regularity order (respectively, fractional singularity order), an orthogonal decomposition of the associated reproducing kernel Hilbert space with respect to domains with fractal boundary is derived. The approach presented is based on the theory of generalized random fields on fractional Sobolev spaces. The orthogo...

The weak-consistency of the wavelet periodogram is established for a class of semiparametric fractal Gaussian random fields with local behavior equivalent to the fractional Brownian motion. This result is derived considering a class of isotropic wavelet functions of Haar type. As a consequence, the consistency of a minimum contrast estimator of the...

This paper addresses the problem of parameter estimation of spatiotemporal long-range dependence models from functional spectral data. Four wavelet-based functional estimation algorithms are proposed to approximate the multidimensional strong-dependence parameter, characterizing the covariance tail behavior of the spatiotemporal non-self-similar mo...

Weak consistency of the wavelet periodogram is established for a class of linear Gaussian random fields, considering a Haar
type isotropic wavelet basis. A minimum contrast estimation procedure is introduced and the weak consistency of the estimator
is derived, following the methodology introduced by Ruiz-Medina and Crujeiras (2011).

This paper introduces new classes of fractional and multifractional random fields arising from elliptic, parabolic and hyperbolic equations with random innovations derived from fractional Brownian motion. The case of stationary random initial conditions is also considered for parabolic and hyperbolic equations.

This paper proposes a two-stage correlated non-linear shrinkage estimation methodology for spatial random processes. A block
hard thresholding design, based on Shannon’s entropy, is formulated in the first stage. The thresholding design is adaptive
to each resolution level, because it depends on the empirical distribution function of the mutual inf...

This paper addresses the introduction and study of structural properties of Hilbert-valued spatial autoregressive processes (SARH(1) processes), and Hilbert-valued spatial moving average processes (SMAH(1) processes), with innovations given by two-parameter (spatial) matingale differences. For inference purposes, the conditions under which the tens...

In this article, we introduce a class of Markov processes whose transition probability densities are defined by multifractional pseudodifferential evolution equations on compact domains with variable local dimension. The infinitesimal generators of these Markov processes are given by the trace of strongly elliptic pseudodifferential operators of va...

In this paper, the effect of the domain geometry on the local regularity/singularity properties of the solution to the trace
of a multifractional pseudodifferential equation on a fractal domain is studied. The singularity spectrum of the Gaussian
solution to this type of models is trivial due to regularity assumptions on the variable order of its f...

A functional statistical analysis of a data panel constituted by 33 companies in the IBEX-35, Spain, during the period 2006 to 2009, is achieved for the investigation of possible changes in the dividend policy. Empirical evidence of positive functional correlation of dividend policy changes with future changes of earnings per share is provided by t...

A general functional class of spatial scalings is introduced, jointly with the logarithmic transformation of the temporal component, to get the convergence to the Gaussian limit distribution of the solution to the heat and Burgers equations with quadratic external potentials, considering weakly dependent Gaussian random initial conditions. The resu...

Fractal Gaussian models play a crucial role in image analysis applications (e.g. biophysics, geophysics, medical imaging data). In this paper, the filtering and reconstruction problems for noisy and blurred homogeneous and heterogeneous fractal functional image sequence data are studied. Specifically, conditions under which a stable solution to the...

Functional classification of fractal temporal gene expression data is per- formed in terms of logistic regression based on the wavelet-vaguelette decomposition of the temporal gene expression curves. The fractality features of the gene expres- sion profiles comes from the stochastic evolutionary forces acting on genomes. The noise level introduced...

Pseudodifferential evolution models have been widely used in the description of biological, geophysical and environmental
systems. We consider the case where functional sample information is available from such systems. Specifically, the observation
model is defined in terms of a sequence of spatial realizations of the process of interest, solution...

Functional data models provides a suitable framework for the statistical analysis of several environmental phenomena involving
continuous time evolution and/or spatial variation. The functional autoregressive model of order p, p ≥ 1, (FAR(p)) extends to the infinite-dimensional space context the classical autoregressive model AR(p) (see, for exampl...

En este artículo se presenta una investigación que busca caracterizar las creencias que tienen algunos profesores de preescolar y primaria sobre ciencia y tecnología en un contexto rural. La metodología usada fue cualitativa, en función de comprender e interpretar la realidad del escenario y participantes observados. Para la recolección de la infor...

In this paper the problem of functional filtering of an autoregressive Hilbertian (ARH) process, affected by additive Hilbertian
noise, is addressed when the functional parameters defining the ARH(p) equation are unknown. The maximum-likelihood estimation
of such parameters is obtained from the implementation of an expectation-maximization algorith...

Long-memory and strong spatial dependence are two features which can arise jointly or separately depending on the tail behavior of the temporal and spatial covariance functions of a given spatiotemporal process. Under certain conditions, such a behavior can be related to the variation of temporal and spatial frequencies in a neighborhood of the ori...

For a suitable scaling of the solution to the one-dimensional heat equation with spatial-dependent coefficients and weakly
dependent random initial conditions, the convergence to the Gaussian limiting distribution is proved. The scaling proposed
and methodology followed allow us to obtain Gaussian scenarios for related equations such as the one-dim...

The philosophy of Fan (1996) and Fan and Lin (1998) is adopted in the formulation of significance tests for comparing autoregressive
Hilbertian processes. The discrete wavelet domain is considered to derive the test statistic based on thresholding rules.
The results derived are applied to the statistical analysis of spatial functional data (SFD) se...

Estimation of the long-range dependence parameter in spatial processes using a semiparametric approach is studied. An extended formulation of the averaged periodogram method proposed in Robinson [1994. Semiparametric analysis of long memory time series. Ann. Statist. 22, 515–539] is derived, considering a certain homogeneous and isotropic behaviour...

In this paper, a class of spatiotemporal random field models defined as mean-square solutions of fractional versions of the
stochastic heat equation are considered. Different sampling schemes in space and time are introduced to solve the problem
of estimation of fully parameterized spatiotemporal random fields.