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M. D. Ruiz-Medina

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

26 records · Page 2Linked to original sources
arXiv2018

Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

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 componentwise estimator of the residual autocorrelation operator. When the dependence structure of the functional error term is unknown, a plug-in generalized least-squared regression parameter estimator is formulated. Its strong-consistency is proved as well. A simulation study is undertaken to illustrate the performance of the presented approach, under different regularity conditions. An application to financial panel data is also considered.

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arXiv2017

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

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 operator are unknown, and the autocorrelation operator does not admit a diagonal spectral representation with respect to the eigenvectors of the autocovariance operator.

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arXiv2017

Space-time fractional diffusion of Riesz-Bessel type on regular bounded open domains

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 spatiotemporal Hölder continuity, in the mean-square sense, of the formulated solution is obtained, under suitable conditions, from the asymptotic properties of the Mittag-Leffler function, and the asymptotic order of the eigenvalues of a fractional polynomial of the Dirichlet negative Laplacian operator on such bounded open domains.

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arXiv2016

Rosenblatt distribution subordinated to gaussian random fields with long-range dependence

The Karhunen-Loève 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 of this new distribution are obtained. Specifically, its series representation in terms of independent chi-squared random variables is given, the asymptotic behavior of the eigenvalues, its Lèvy-Khintchine representation, as well as its membership to the Thorin subclass of self-decomposable distributions. The existence and boundedness of its probability density is then a direct consequence.

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arXiv2015

Functional Analysis of Variance for Hilbert-Valued Multivariate Fixed Effect Models

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 the regression. Under suitable linear transformation of the correlated functional data, the distributional characteristics of these statistics, their moment generating and characteristic functions, are derived. Fixed effect linear hypothesis testing is finally formulated in the Hilbert-valued multivariate Gaussian context considered.

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arXiv2015

Non-central limit theorems for random fields subordinated to gamma-correlated random fields

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-Loéve expansion and the Fredholm determinant formula to obtain the characteristic function of its Rosenblatt-type limit distribution. When the Laguerre rank equals one and two, we obtain the multiple Wiener-Itô stochastic integral representation of the limit distribution. In both cases, an infinite series representation in terms of independent random variables is constructed for the limit random variables.

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arXiv2015

On a class of minimum contrast estimators for Gegenbauer random fields

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 consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.

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