Modeling and estimation of some non Gaussian random fields

Abstract

In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields with Gamma and Weibull marginals. Both random fields are obtained transforming a rescaled sum of independent copies of squared Gaussian random fields. For the second case, we propose a random field with t marginal distribution. We then consider two possible generalizations allowing for possible asymmetry. In the first approach we obtain a skew-t random field mixing a skew Gaussian random field with an inverse square root Gamma random field. In the second approach we obtain a two piece t random field mixing a specific binary discrete random field with half-t random field. We study the associated second order properties and in the stationary case, the geometrical properties. Since maximum likelihood estimation is computationally unfeasible, even for relatively small data-set, we propose the use of the pairwise likelihood. The effectiveness of our proposal for the gamma and weibull cases, is illustrated through a simulation study and a re-analysis of the Irish Wind speed data (Haslett and Raftery, 1989) without considering any prior transformation of the data as in previous statistical analysis. For the t and asymmetric t cases we present a simulated study in order to show the performance of our method.