Quantile Regression Model and Its Application Research

Abstract

Quantile regression is a regression analysis method that estimates the parameters of a model by minimizing the weighted sum of absolute residuals. It was introduced by Roger Koenker in 1978. As a complementary and extended approach to the traditional regression method, namely least squares method, quantile regression addresses the limitations of least squares method in the presence of heteroscedasticity and ensures the robustness of quantile regression through its robustness to outliers, which compensates for the weakness of least squares method in dealing with outlier data. In practical applications, quantile regression can provide a more comprehensive reflection of data information and capture the tails of the distribution of the dependent variable, thus overcoming the limitation of least squares method that can only estimate the central tendency of the dependent variable distribution. Moreover, quantile regression provides more reasonable interpretations and prevents biased or even erroneous estimations that can occur when using least squares method. Overall, quantile regression offers a novel regression method that addresses many shortcomings of least squares method. By combining quantile regression with least squares method, we can understand both the central tendency and tail behavior of the dependent variable distribution. The fitting results obtained from quantile regression can also provide insights into the suitability of least squares estimation. Briefly, the combination of both methods yields better results in statistical problems. This paper introduces the principles of quantile regression and further discusses its scope and application, aiming to provide a preliminary summary for a better understanding of quantile regression.