EVALUATING THE ESTIMATION OF REGULARIZED COVARIOGRAMS

Luis Paulo Vieira BRAGA[1]

Cassio ALMEIDA[2]

Claudio BETTINI[3]

§    ABSTRACT:  In this work, we present the effeciency of the approximation  of a regularized variable´s covariogram over a large panel (2D) by the covariogram of a regularization via accumulation of order 2 (montée) of a three-dimensional regionalized variable. The regularized covariogram can be obtained through a numerical approximation of the inverse Fourier transform of the G1 Fourier transform of the regularized covariogram by accumulation of order two of the fitted point covariogram. Such accumulation is obtained through the G3 Fourier transform of the point covariogram by equating two of its coordinates to zero. Two data sets were approached, the first is  simulated according to a Matérn law and the second one is based on observed temperature  values recorded along extensive time periods, over a wide region located in the Brazilian Amazon region. In this area,  we considered the mean values of the daily temperatures in January,  along nine decades, namely,  from 1901-1910 to 1981-1990. Cross validation interpolations as well as simulations were performed, which were compared with the true values observed in each decade, thus checking the accuracy of the approximation and the range of the temperature variation .

§    KEYWORDS: Change of support; regularization; non-separable space-time models; geostatistics; global warming.



[1]Instituto de Matemática, Universidade Federal do Rio de Janeiro - UFRJ, CEP 21945-970, Rio de Janeiro, RJ, Brasil, E-mail: lpbraga@im.ufrj.br

[2]Escola Nacional de Ciências Estatísticas, Instituto Brasileiro de Geografia e Estatística - IBGE, CEP 20231-050, Rio de Janeiro, RJ, Brasil, E-MAIL: cassiofreitas@ibge.gov.br

[3]Instituto de Geociências, Universidade Federal do Rio de Janeiro – UFRJ, CEP 21949-900, Rio de Janeiro, RJ, Brasil, E-mail: bettini@geologia.ufrj.br