Some Estimation methods for the two models SPSEM and SPSAR for spatially dependent data

Abstract

ABSTRUCT

In This Paper, some semi- parametric spatial models were estimated, these models are, the semi – parametric spatial error model (SPSEM), which suffer from the problem of spatial errors dependence, and the semi – parametric spatial auto regressive model (SPSAR). Where the method of maximum likelihood was used in estimating the parameter of spatial error          ( λ ) in the model (SPSEM), estimated  the parameter of spatial dependence ( ρ ) in the model ( SPSAR ), and using the non-parametric method in estimating the smoothing function m(x) for these two models, these non-parametric methods are; the local linear estimator (LLE) which require finding the smooth parameter ( h ) according to the cross validation criterion ( CV ), the Local linear two step estimator  after removing the effect of the spatial errors dependence , once using variance- covariance spatial matrix of errors ( Ω )using kernel function(LLEK2) and other through the use of variance- covariance spatial matrix of errors ( Ω^* ) using cubic B-Spline estimator (LLECS2), to remove the effect of the spatial errors dependence, also the Local linear two step estimator using Suggested kernel estimator, once using variance- covariance spatial matrix of errors using kernel estimator (SUGK2), and other through the use of variance- covariance spatial matrix of errors using cubic B-Spline estimator (SUGCS2) to removing the effect of the spatial errors dependence.

From the simulation experiment, with a frequency of 1000 times, for three sample sizes, three levels of variance, for two model, and Calculate the matrix of distances between the sites of the observations through the Euclidean distance, the two estimated methods mentioned above were used to estimate (SPSEM) and (SPSAR) models, using the spatial Neighborhoods matrix modified under the Rook Neighboring criteria. Comparing these methods using mean absolute percentage error (MAPE) turns out that the best method for the SPSEM) model is (SUGCS2) method, and for (SPSAR) model is (LLECS2) method.