ABSTRACT
In this research been to use some of the semi-parametric methods the based on the different function penalty as well as the methods proposed by the researcher because these methods work to estimate and variable selection of significant at once for single index model including (SCAD-NPLS method , the first proposal SCAD-MAVE method , the second proposal ALASSO-MAVE method ) .As it has been using a method simulation time to compare between the semi-parametric estimation method studied , and various simulation experiments to identify the best method based on the comparison criteria (mean squares error(MSE) and average mean squares error (AMSE)).
And the use of real data again to verify the performance of semi-parametric methods indeed the practical , was reached the best method for
estimate and variable selection of semi parametric single index model is the second method proposed (ALASSO-MAVE) for each of the simulation experiments of the first semi -parametric single index model and real data .
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