The Research And The Intergrated Application Of Ridge Regression And Quantile Regression

Ridge regression is a statistical method to solve the multicollinearity amongindependent variables, it indirectly solve the problem by constraint length factor. Inpractical problems, there are many factors that affect a thing, so multicollinearityinevitably exist between them, using ridge regression can eliminate multicollinearityon data to establish a stable model. Quantile regression is a basic tool for estimatingconditional quantiles of a matter, it not only has the excellent properties of samedegeneration, progressive, robustness, also can measure the impact of those factorswhich effect the matter at different quantiles, so can catch the information of thematter comprehensively.In this paper, firstly the mathematical thinking of ridge regression and quantileregression were introduced，the generalized ridge regression was proved a biasedestimation, compression estimate, and three properties of quantile regression wascertificated, the same degeneration, progressive, robustness. Secondly, themathematical models of the two methods were established respectively. Finally, the ofShanghai composite index data listed in paper were researched and analyzed by usingthe mathematical model of ridge regression, reflecting the advantages of ridgeregression in processing the kind of data with multicollinearity. The mathematicalmodel of quantile regression was used to analyze Zhangqukeji stockdata listed inpaper, through the results of significance test and Wald test, knowing the effects of theestablished model at different quantiles were not excellent, the interpretation of thedependent variable did not have the guiding significance, and did not reflect theadvantages of quantile regression, at last it was proved that the multicollinearitybetween independent variables affect the model effect.On the basis of the study of ridge regression and quantile regression respectively,The combined application of the two methods was studied to explore a way thatquantile regression method process with multiplecollinear data. Firstly, ridgeregression was carried out on the data to select the independent variables, thenquantile regression was used these independent variables which were screenedsuccessfully, this not only greatly weakened the impact of the multicollinearitybetween the independent variables in regression equation, also obtain regressionequations at different quantiles, and then through significance test results and thechange of independent variable coefficients research the influence of the independentvariables on dependent variable, the change of the influence, then given thecomprehensive analysis on the dependent variable. In the process of ridge regression,some independent variables were directly eliminated which lead the multicollinearityin data, it will lost a lot of useful information that used explaining the dependentvariable, so quantile regression analysis on the dependent variable was used to the independent variable which was removed individually, using the information in thedata to analyze fully. In processing multicollinearity data, the model which wasestablished by the combined method of ridge regression and quantile regressioneffectively have better performance than the model which was established by quantileregression directly, and have more guiding significance to practical applications.