Performance Comparison of the Quantile Regression Coefficient Estimation with Outliers

Abstract

This research aims to compare the coefficients estimation performance of quantile regression (QR) at different percentiles and simple regression (SR) for dataset with outliers. Five quantile positions were considered comprising QR(10)th, QR(25)th, QR(50)th, QR(75)th and QR(90)th. These were obtained by modifying the probability density functions for the kernel function adjustment under errors. The results were then compared with the simple regression coefficient estimation. After applying variety situations of the simulation, the mean absolute error (MAE) was used as criteria for consideration. The results showed that although the best performance model for large sample size was the SR, it still gave the best performance for small sample size as well as QR(25)th and QR(50)th models. Furthermore, the QR(25)th and the QR(50)th models were the most efficient estimation of the quantile regression coefficients with outliers for moderate sample size. They also indicated that there were changes scattered around zero value when the sample size was small. Comparing between the SR model and the QR(50)th model for every sample size, it was found that their model coefficients are slightly different. Considering kurtosis and skewness for the SR and all QR models, the results revealed that both values increased with small sample size. Then, they decreased with moderate sample size and increased again with large sample size. Therefore, the quantile regression coefficient estimation is effective in relationship analysis and provides estimates that are more accurate than one answer and suitable as an alternative analysis for skewed data.