Wavelet Estimation of Semi-parametric Regression Model

Abstract

The semi-parametric regression model combines parametric and nonparametric regression. However, non-parametric estimation may provide flexible solutions to the problems suffers by the regression model, but the problem of dimensionality that this estimator suffers, which occurs due to the increasing number of explanatory variables, still remain, this, in turn, may reduce the accuracy of the estimation process. Estimate the non-parametric part of the semi-parametric models that can be studied using conventional non-parametric methods such as the Spline Smoothing and Kernel Smoothing. However, there are other non-parametric methods that can be used, therefore, in this paper, the semi-parametric regression model was estimated by employing the wavelet estimate for the soft threshold, according to the "Speckman" method, and then comparing it with the two methods, Nadaraya-Watson and Local Linear, through the implementation of simulation experiments that included different sample sizes and threshold values. The parametric part estimation of the partially linear model according to the least-squares method was not identical to those estimates using the Speckman method, that is because the least-squares method was not appropriate for the uneven nature of the number of weekly work hours. Simulation experiments have demonstrated the efficiency of the wavelet estimation method and its superiority over other methods. The above estimation methods were applied to real data related to the study of the production value for the public industrial sector in Iraq, and some factors affect it, such as the value of industrial supplies, the total wages of workers, and the number of workers.