Testing the Equality of Two Parametric Quantile Regression Curves : The Application for Comparing Two Data Sets

This study aims to compare the different between two data sets that having the relationship between the dependent and independent variables at each quantile using testing the equality of two parametric quantile regression functions, the conditional quantile regression and the conditional mean regression function are considered. The influence of outliers and the distribution of errors is also examined through a test statistic that is in the form of the empirical distribution function, applying the bootstrapping principle in the estimation of the critical value of the test statistic. The results show that the power of the test becomes greater as the sample size increases. However, with variables such as heavy-tailed distribution of errors or outliers, the conditional median regression function is more robust. An analysis of the actual data indicates consistent findings.