Euclidean likelihood method for space time covariance function using parallel computation / Víctor Roberto Morales Oñate.

Doctor en Estadística.

Today, statistical analyses with one or more variables, observed in space and time are useful in different areas, such as environmental sciences and engineering to name a few. Random fields are the mathematical foundation for the statistical analyses of this kind of data which allows to describe their marginal behavior and to assess the dependence structure inside the data. Three fundamental steps are needed when analyzing such data using random fields: modeling, estimation and prediction. We focus on estimation. In particular, we develop estimation methods for spatio temporal Gaussian random fields observed on a large number of location sites and/or temporal instants. Maximum likelihood, in this case, is computationally unfeasible. This thesis elaborates an Euclidean likelihood method for space time covariance function using parallel computation in order to reduce the computation burden for the estimation of a spatio-temporal random field. The method is called STBEU which stands for space-time blockwise euclidean likelihood. The method was implemented in R and it was boosted using parallel computation with the OpenCL framework. An R package called STBEU was created for reproducibility purposes. We also study the asymptotic properties of the method and show, through numerical simulation and real data-set estimation, that STBEU offer a good balance between statistical efficiency and computation complexity.