A flexible Clayton-like spatial copula with application to bounded support data

The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distributions. However, this kind of model can potentially be too restrictive since it expresses a reflection symmetric dependence. In this paper, we propose a new spatial copula model that makes it possible to obtain random fields with arbitrary marginal distributions with a type of dependence that can be reflection symmetric or not. Particularly, we propose a new random field with uniform marginal distributions that can be viewed as a spatial generalization of the classical Clayton copula model. It is obtained through a power transformation of a specific instance of a beta random field which in turn is obtained using a transformation of two independent Gamma random fields. For the proposed random field, we study the second-order properties and we provide analytic expressions for the bivariate distribution and its correlation. Finally, in the reflection symmetric case, we study the associated geometrical properties. As an application of the proposed model we focus on spatial modeling of data with bounded support. Specifically, we focus on spatial regression models with marginal distribution of the beta type. In a simulation study, we investigate the use of the weighted pairwise composite likelihood method for the estimation of this model. Finally, the effectiveness of our methodology is illustrated by analyzing point-referenced vegetation index data using the Gaussian copula as benchmark. Our developments have been implemented in an open-source package for the \textsf{R} statistical environment

Asymptotically equivalent prediction in multivariate geostatistics

Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. 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 typically 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 Matérn 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

Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model. Then consistency and asymptotic distribution for the microergodic parameters are established. A simulation study is presented in order to compare the finite sample behavior of the maximum likelihood estimator with the given asymptotic distribution

A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers

In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavy-tailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East

Modelling Point Referenced Spatial Count Data: A Poisson Process Approach

Gaussian random field, Gaussian copula, Pairwise likelihood function, Poisson distribution, Renewal proces

Concatenative morphology and non-concatenative morphology : from the morphological principle to the prosodic principle

No estudo dos processos de formação de palavras, a morfologia tem papel fundamental, pois nos ajuda a entender os constituintes morfológicos, as partes que formam uma palavra. Ao lado de processos tradicionais, como a composição e a derivação, há processos ditos marginais, que convocam, além dos princípios morfológicos, princípios prosódicos. Os processos tradicionais pertencem à morfologia concatenativa, e os processos marginais, à morfologia não concatenativa. Os não concatenativos redefinem o conceito tradicional de “morfema”, pois há elementos (ditos não morfêmicos) que não atendem às condições de morfema apregoadas pela gramática, como significação e recorrência. Para entender a concepção desses novos constituintes morfológicos, objetivamos, neste artigo, mostrar as diferenças entre as morfologias concatenativa e não concatenativa, destacando três processos que se baseiam no princípio morfofonológico: cruzamento vocabular, truncação e siglação.Morphology is fundamental in the study of word formation processes. It helps us to understand the morphological constituents responsible for word formation. In addition to traditional processes, such as composition and derivation, there are other non-traditional processes, which are based on prosodic principles. Traditional processes belong to concatenative morphology and prosodic processes belong to non-concatenative morphology. Non-traditional processes redefine the traditional concept of “morpheme”, because there are elements (called non-morphemics) that do not satisfy the morpheme conditions defended by grammar, such as meaning and recurrence. In order to understand the conception of these new morphological constituents, in this article, we aim to expose the differences between concatenative and non-concatenative morphologies, using three processes that are based on the morphophonological principle: lexical blend, truncation and acronymization