Proposta de correção do viés na estimação da semivariância do resíduo na presença de tendência

Abstract

The aim of geostatistical analysis is the prediction of data in locations that were not sampled in the region of a phenomenon with spatial dependence. Geostatistics allows implementation of a prediction or kriging map that characterizes the spatial variability of this phenomenon. The quality of this map, as well as all products of geostatistical analysis depends on quality of semivariances estimation. For situations that mean of regionalized variable is not constant, one can resort to prediction with universal or regression kriging. However, the semivariance of residuals or predicted errors, used by both types of kriging presents bias, underestimating values of semivariance of errors, with significant loss in modeling of spatial variation. Therefore, efforts have been made to correct the bias in semivariance of residuals. Thus, the present work was done with objective of developing a methodology to correct such bias, termed criterion IRWGLS (Iteratively Re-weighted Generalized Least Squares) with bias correction, and implement it in software R. The semivariance models adjusted according to semivariogram were used to compose error covariance matrix. To estimation of parameters of these models, the criteria of ordinary and generalized least squares were used and a bias correction according to the proposed methodology. To evaluate the performance of the proposed methodology, an analysis was performed with three data sets that were submitted to a validation test. The results obtained showed an effective improvement in quality of estimation of parameters in the semivariance model. In addition, use of the proposed methodology potentiated bias correction in semivariance model considered as most adequate to describe the spatial variability of phenomenon, fact perceived by highest percentage increase in mean values of estimated semivariances, which reached 9.96 % in one sample set. The proposed methodology has advantage of being of general validity and, together with experience of specialists with knowledge of physical aspect of the phenomenon and statisticians, it constitutes an advance so that the objective of geostatistical analysis isreached with more accuracy and precision.