Applied Nonparametric Regression Methods as Alternatives to the Linear Regression Methods (Comparative Study)

Linear regression methods impose strong constraints on regression models, especially on the error terms where it assumes that it is independent and follows normal distribution, and this may not be satisfied in many studies, leading to bias that cannot be ignored from the actual model, which affects the credibility of the study. We present in this paper the problem of estimating the regression function using the Nadarya Watson kernel and k- nearest neighbor estimators as alternatives to the parametric linear regression estimators through a simulation study on an imposed model, where we conducted a comparative study between these methods using the statistical programming language R in order to know the best of these estimations. Where the mean squares errors (MSE) was used to determine the best estimate. The results of the simulation study also indicate the effectiveness and efficiency of the nonparametric in the representation of the regression function as compared to linear regression estimators, and indicate the convergence of the performance of these two estimates.

Compare between two interpolation methods (Kriging, IDW) for predicting spatial distribution of nitrate NO3 - in groundwater of Estern Ghouta- Damascus

Groundwater is one of the major sources of exploitation in arid and semi-arid regions, Thus for protecting groundwater quality, data on spatial and temporal distribution are important. Geostatistics methods are one of the most advanced techniques for interpolation of groundwater quality. In this research, IDW, Kriging methods were used for predicting spatial distribution of nitrate NO3 -. Data were taken from 21 wells study within eastern Damascus's Ghouta. After normalization of data, variograme was drawn. The less RSS was used, so Spherical model was the best. By using cross-validation and RMSE, the best method for interpolation was selected; Results showed that Kriging method is superior to IDW method. there is a big spatial dependence for nitrate variable that amounts to 2.2 %. Finally, maps of distribution of nitrate in groundwater were executed by Kriging method, in addition to executed maps that show goodness of groundwater for drinking and irrigation. Then it was prepared map of Probability Map of nitrate at threshold 50 mg/l.