Studying some approaches to estimate the smoothing parameter for the nonparametric regression model

Abstract

Several previous studies have addressed various topics in regression analysis and estimation of the appropriate regression equation. It assumes that there is a known and pre-defined function relationship between variables. The studied variables are known for distribution using some known methods of estimation, such as the ordinary least squares method (OLS) and the maximum likelihood method (MLE). The parameter model can be estimated due to problems arising from the application of the parameter model, because the theoretical assumptions of the model application are not met. Here, we adopted another method of estimating the regression equation using non-parametric methods. It proved its efficiency and ability to analyze data without the need for prior assumptions on the model. Based on the adopted data, it determines the functional shape of the studied population. Therefore, the aim of this research is to use non-parametric smoothing methods to approximate the non-parametric regression function to the real regression function. This is done by using some non-parametric smoothing methods such as Kernel methods by Nadaraya-Watson and the method of the nearest neighbor (K-Nearest-Neighbor) depending on the bandwidth (h).The study uses the experimental method of simulation on two test functions. Three sizes of sample data (n = 15, n = 50, n = 75) and three values for random error variance (σ^2=0.5),(σ^2=1),(σ^2=2) are assumed. Kernel methods based on Nadaraya-Watson Smoothed Cross Validation are the best choice for the bandwidth of the first test function. On the other hand, Least Squared Cross Validation method for the forensic crossing is the best choice for the bandwidth of the second test function. The second one was better than the neighbor method closest to the first test function.