Abstract
In this paper, we used many forms of kernel functions with minimum average variance estimation (MAVE) method [Xia2002] we called the proposed methods (MAVE-Biweight), (MAVE-Epanechnikov ) and .(MAVE-Gaussian ) for estimation the parameters and the link function of the single – index model (SIM) comparing with other methods of estimation . to evaluate the performing of the various methods s simulation and a real data have been used, conclusions showed that the (MAVE- Gaussian) method in this paper gave better results compared with other methods depending on the mean squared error (MSE) and mean Absolute error (MAE) criterion for comparison.
Highlights
single – index model (SIM) are widely used in sciences of applied quantitative
SIMs are widely used in sciences of applied quantitative
The objective of this paper is identify the best method based on the Two comparison criterion mean squared error (MSE) and mean absolute error (MAE)
Summary
SIMs are widely used in sciences of applied quantitative. SIMs looking for a single linear combination of Xs variables that can catch information on a relation between Y and X, to avoid the curse of dimension the model (SIM) can be written as :. By the covariates and to fit a non-parametric curve To their linear combinations .this is lead to the single – index model (SIM): yi = g (xiT β) + ∈i , i = 1,2,...,n Where g(xiT β) is a smooth unknown function , xi is a p×1 vector of covariates , β = 1) The semi-parametric single – index model can avoid the problem of .error distribution misspecification. Less restrictive than parametric models for conditional mean functions, such as linear models and binary probit models, use of a semi-parametric single – index model reduces the risk obtaining misleading results.
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