Using Some Wavelet Shrinkage Techniques and Robust Methods to Estimate the Generalized Additive Model Parameters in Non-Linear Models

Abstract

In this paper, the method of estimating the Generalized Additive Models (GAM) was highlighted, and a proposed robust weighted composition was found by combining the robust M method with the smoothing splines to estimate the Robust Generalized Additive Model and its notation is (RGAM). This estimator is used to deal with the effect of the presence of outliers in the data that do not fit into the overall data pattern by relying on some of the weight functions of the robust M method. Wavelet Shrinkage technique is used as well, which has been proposed as a smoothing of data using several types of wavelet filters in calculating the discrete wavelet transformation and relying on it in estimating the wavelet generalized additive model symbolized by (WGAM). In the case of using the simulation method, when data is contaminated with distributions ((t) Dis., Exp. Dis.) And with contamination rates (5%, 15%, 35%) and with sample sizes (50,150,300) it is noted that the smoothing method is with the Bisequare weight (BRGAM). It had a better performance compared to the rest of the methods for the simulated scenarios covered. The GCV criterion showed a marked advantage over other criteria, especially when estimating the model in the proposed robust M (RGAM) model. Some statistical criteria have been adopted. These criteria of the Generalized Additive Model (GAM) is used to compare estimation methods, the proposed methods were tested on simulation experiments as well as on real data collected from Ibn Sina Learning Hospital on cases of short stature, and the RGAM method gave the best results compared to the ordinary GAM and WGAM methods, and that by obtaining the smallest GCV value, this is because it is responsible for selecting the most suitable smoothing parameter for the smoothing spline estimator.

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

“…Identity matrix GCV method is same as the CV method that does not require variance information 2  [29]- [30].…”