A Cauchy Transformation approach to the Robustness of Quantile Regression Model to Outliers

Abstract

The main advantage of quantile regression models had over OLS is their robustness to outliers. This is because quantile regression models are insensitive to outliers and skewed distributions. This very property of quantile regression model is the same with the sample quantile. This work was done to examine the robustness of quantile regression model to outliers. Data analysis was done usingreal life data set on fuel consumption (in miles per gallon), in highway driving as the response variable. Extreme values where inserted to create outliers in the response variable data set. Car weight, length, wheel base, width, Engine size and horse power are the explanatory variables used in the analysis with a sample size of 91. The standard Cauchy distribution was used to transform the quantile regression model. The results show that the graphs of the mean square errors clustered around the zero line in all the study quantiles, also the descriptive results show that the residual means is equal to the residual medians and equal to zero. The skewness of the residuals approximates to zero across all the study quantiles, while the kurtosis approximates to 3, both the residual standard deviations, mean square errors and root mean square errors approximate to zero across all the study quantiles.  From the results of the analysis, it can be concluded that quantile regression model is insensitive to outliers.