Quantile Regression And Its Application

Quantile regression is a kind of new regression method which estimates parameters of model by minimizing a kind of weighting absolute residual. It was introduced by Roger Koenker in1978.As a supplement of classic regression method--least squares, quantile regression can handle models with heteroscedasticity, which can’t be done with least squares. We can get the robustness of quantile regression through the robustness of quantile. Least squares were not robust enough in dealing with models with outliers, while quantile regression can do it well. In practical application, quantile regression can reflect information of data more completely. Instead of just focusing on conditional mean of response variable which least squares do, quantile regression can get information of tails. And we can have a more reasonable interpretation by using quantile regression. Least squares often give unilateral or even wrong results, which can be corrected by quantile regression. In a word, quantile regression is a really new regression method which can remedy limitation of least squares. We should combine least squares with quantile regression to get a more complete description. We can even judge the rationality of least squares estimates by quantile regression results. Least squares do have its advantage. If observational noise is normally distributed, least-squares method can give a perfect result. There will be better results if using least squares and quantile regression at the same time.The paper introduces the origin of regression, theory of least squares and theory of quantile regression. The main body includes the origin of quantile, properties of quantile, quantile regression theory and two important properties of quantile regression estimators. Then a comparison between least square and quantile regression is given to find out their difference and advantages. In Chapter four, quantile regression is used to analyze Shanghai and Shenzhen stock data and Chinese agricultural input and output data. Then a set of artificial data was created to reflect the robustness of quantile regression. Specially, chapter four shows not only how to analyze data with quantile regression, but also its properties and advantages, such as more information, interpretation of tails and robustness with outliers.