Nonparametric Quantile Regression Estimation Of Income And Expenditure Of Urban Residents

With With the development of statistical analysis, more and more researchers focusedon data modeling and statistics analysis, because the design of models is the basis of deeperresearch, an excellent model can achieve the best fitting of the object analyzed, so that a morecomprehensive and accurate characteristics of the object analyzed can be grasped, and deeperresearch and effective conclusions can be make.In all kinds of statistical methods, the least squares method is widely used in research ofparametric and nonparametric models because of brevity and accuraty. However, no methodis perfect. The least squares have drawbacks when datas have outliers and heteroscedasticity,because of its own limitations. The Quantile Regression improves and supplies the problemeffectively, and shows excellent stability in estimation of parametric and non-parametricmodel. This paper focuses on the theory of quantile, nonparametric quantile regressionmodel, local polynomial estimation methods and their practical applications and researches indeep. It carried out the following works:Firstly, the paper introduces the research background, the formation and developmentprocess of the quantile regression theory. As can be seen, the application of quantile isexpanded by scholars continuesly, fully illustrated that the quantile regression can be appliedin various fields, which is saying the study of quantile regression is of great significance inanother way.Secondly, the paper introduces the theoretical basis in detail, namely, the definition ofquantile regression and the fundamental and the relative principles. The paper also expandsthe usefulness of quantile regression, finds out the suitable modle, nonparametric quantileregression modle, and explanes in detail.Again, income and expenditure of residents in230cities are modeled and analyzed bylocal polynomial method, the most commonly used method in nonparametric modelestimation, as well as quantile regression techniques. Compared with the result of the leastsquares estimation, a conclusion can be make, which is, the nonparametric quantileregression is better than the least squares estimation when the data is big and in unnormaldistribution and can provide more information to facilitate statistical analysis to get the rightconclusions. Finally, by use of nonparametric quantile regression, the conclusion is not only aextension of applications using nonparametric quantile regression, but also a useful referenceon the field of economics research.