The single index model is regard as a semiparametric model; this kind of models is more flexible and less restrictive than parametric models of conditional mean functions. In this paper we discuss the estimation of error distribution depending on the single index model, our application focuses on bricks production for several factories across Iraq. We compare three estimation methods (Semiparametric Least Squares (SLS), Refined Outer Product of Gradients (rOPG) and Refined Minimum Average Variance Estimation (rMAVE). Then the error distribution is estimated by using two approaches, the empirical distribution and Kernel distribution functions. The results indicate that the rOPG performs best for the single index model, while the empirical distribution function provides the more accurate estimation for error distribution. We use the normal distribution test to certify that the residuals follow a normal distribution for the used single index model estimation methods. Additionally, we compare our results with the multiple linear regression models to give an insight to about the correct specification of the appropriate model.
Keywords
Semiparametric Least SquaresRefined Minimum Average Variance EstimationRefined Outer Product of GradientsThe empirical distributionKernel distribution function.
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