The Research To Eliminate Multicollinearity Based On Kernel Principal Component Regression

Regression analysis is a commonly applied statistical analysis and prediction methodin economics, business administration, social sciences, engineering technology, medicalscience and biological sciences. In the regression analysis, it often leads to severely affectof estimate of regression coefficients. If multicollinearity is existed between independentvariables, the estimated variance is expanded, and stable regression model is destroyed.Therefore, eliminating multicollinearity is an important part to estimating coefficient.Currently, the main regression methods to solve the problem of multicollinearity areridge regression, principal component regression and partial least squares regression, theyare linear regression methods. Nonlinear regression method to solve the existence of acomplex social reality has been rarely referred.Firstly, it summarizes the current method to solve multicollinearity existing researchand treatment. Secondly, it introduces the theory of nuclear methods and kernel principalcomponent regression. From the view of nonlinear, we propose the method by KPCR todeal with the problem of multicollinearity. We give the specific implementation steps toeliminate nonlinearity by kernel principal component regression.Finally, through data simulation and empirical studies, it is found that the extractionby kernel principal component regression will improve as variable increase in addressingthe problem of linear regression, contrary by principal component regression. So it hasmore advantage by kernel principal component regression to handle multicollinearity.The extraction of kernel principal component analysis is superior to deal with the issue ofnonlinear regression, extracting a kernel principal component can reach more than90%,and thus kernel principal component regression eliminates the multicollinearity well freefrom unreliable and inaccurate regression model.