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Author (down) Khosravi, M.; Leiva, V.; Jamalizadeh, A.; Porcu, E.
Title On a nonlinear Birnbaum-Saunders model based on a bivariate construction and its characteristics Type
Year 2016 Publication Communications In Statistics-Theory And Methods Abbreviated Journal Commun. Stat.-Theory Methods
Volume 45 Issue 3 Pages 772-793
Keywords Data analysis; Elliptically contoured distributions; Likelihood and Monte Carlo methods; Linear and nonlinear skew-elliptic distributions
Abstract The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew-t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.
Address [Khosravi, Mohsen; Jamalizadeh, Ahad] Shahid Bahonar Univ Kerman, Dept Stat, Kerman, Iran, Email: victorleivasanchez@gmail.com
Corporate Author Thesis
Publisher Taylor & Francis Inc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0361-0926 ISBN Medium
Area Expedition Conference
Notes WOS:000368695100016 Approved
Call Number UAI @ eduardo.moreno @ Serial 576
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Author (down) Faouzi, T.; Porcu, E.; Kondrashuk, I.; Bevilacqua, M.
Title Convergence arguments to bridge cauchy and matern covariance functions Type
Year 2023 Publication Statistical Papers Abbreviated Journal Stat. Pap.
Volume Early Access Issue Pages
Keywords Mellin-Barnes transforms; Positive definite; Spectral densities; Random field
Abstract The Matern and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Matern family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Matern family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0932-5026 ISBN Medium
Area Expedition Conference
Notes WOS:000936708800003 Approved
Call Number UAI @ alexi.delcanto @ Serial 1753
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Author (down) Faouzi, T.; Porcu, E.; Bevilacqua, M.
Title SPACE-TIME ESTIMATION AND PREDICTION UNDER FIXED-DOMAIN ASYMPTOTICS WITH COMPACTLY SUPPORTED COVARIANCE FUNCTIONS Type
Year 2022 Publication Statistica Sinica Abbreviated Journal Stat. Sin.
Volume 32 Issue 3 Pages 1187-1203
Keywords Fixed-domain asymptotics; microergodic parameter; maximum likelihood; space-time generalized wendland family
Abstract We study the estimation and prediction of Gaussian processes with spacetime covariance models belonging to the dynamical generalized Wendland (DGW) family, under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Matern class.

Our results are presented in two parts. First, we establish the strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated with the DGW covariance model, under fixed-domain asymptotics. The second part focuses on optimal kriging prediction under the DGW model and an asymptotically correct estimation of the mean squared error using a misspecified model. Our theoretical results are, in turn, based on the equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. The technical results are provided in the online Supplementary material.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1017-0405 ISBN Medium
Area Expedition Conference
Notes WOS:000818975200001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1599
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Author (down) Bevilacqua, M.; Camano-Carrillo, C.; Porcu, E.
Title Unifying compactly supported and Matern covariance functions in spatial statistics Type
Year 2022 Publication Journal of Multivariate Analysis Abbreviated Journal J. Multivar. Anal.
Volume 189 Issue Pages 104949
Keywords Gaussian random fields; Generalized wendland model; Fixed domain asymptotics; Sparse matrices
Abstract The Matern family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matern case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported.

More importantly, we show that the proposed covariance family generalizes the Matern model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matern model with an extra-parameter that allows for switching from compactly to globally supported covariance functions.

Our numerical experiments elucidate the speed of convergence of the proposed model to the Matern model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0047-259X ISBN Medium
Area Expedition Conference
Notes WOS:000759649300026 Approved
Call Number UAI @ alexi.delcanto @ Serial 1542
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Author (down) Bachoc, F.; Porcu, E.; Bevilacqua, M.; Furrer, R.; Faouzi, T.
Title Asymptotically equivalent prediction in multivariate geostatistics Type
Year 2022 Publication Bernoulli Abbreviated Journal Bernoulli
Volume 28 Issue 4 Pages 2518-2545
Keywords Cokriging; equivalence of Gaussian measures; fixed domain asymptotics; functional analysis; Generalized Wendland; Matern; spectral analysis
Abstract Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geo-statistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typ-ically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a d-dimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1350-7265 ISBN Medium
Area Expedition Conference
Notes WOS:000843190100015 Approved
Call Number UAI @ alexi.delcanto @ Serial 1639
Permanent link to this record