A comparative study of detrended spatial data prediction using support vector and polynomial regression methods with universal kriging

Abstract

Stationarity is a fundamental assumption in the analysis of correlated data. The presence of a trend in observations causes non-stationarity in the mean. Detecting and eliminating the trend is one of the initial steps in such analyses. So far, methods such as polynomial regression, spline, etc. have been used to model the trend. Support vector regression is a new and efficient methodology in the area of modeling and function estimation. Therefore, it can be a suitable proposed option for modeling the trend in spatial data that have non-stationarity in terms of the mean. An extensive simulation study has been conducted to compare the support vector regression method with polynomial regression in modeling the trend and then the effect of these models in predicting and comparing the results with universal kriging. For this purpose, first, a dataset was generated on an irregular grid Gaussian random field with zero mean and then three simple linear, quadratic and nonlinear models were added to them. Also, the proposed method was implemented on a real dataset. The results showed that if the parameters of the support vector regression method are appropriately selected, the proposed method has a good performance in both trend modeling and prediction.