Semi-parametric regression models have been studied in a variety of applications and scientific fields due to their high flexibility in dealing with data that has problems, as they are characterized by the ease of interpretation of the parameter part while retaining the flexibility of the non-parametric part. The response variable or explanatory variables can have outliers, and the OLS approach have the sensitivity to outliers. To address this issue, robust (resistance) methods were used, which are less sensitive in the presence of outlier values in the data. This study aims to estimate the partial regression model using the robust estimation method with the wavelet threshold and the PLM estimation method with the Speakman estimation and Nadarya-Watson smoothing, using simulation experiments at different sample sizes and contaminated ratios.
The mean square error criterion was employed to compare the two methods. The robust method is more efficient in obtaining robust estimators than the PLM estimation method
