The Application Investigation On SIR Dimension Reduction Method And Semi-parametric Additive Regression

A large number of high-dimensional data have emerged in the fields of economy, finance and medicine, due to the advent of information technology and the development of huge amounts of data. The traditional statistical methods will encounter many problems in dealing with high-dimensional data, non-parametric models which developed in recent years also will suffer the curse of dimensionality in analysis of high-dimensional data. Therefore, in statistics emerged a series of dimension reduction methods, such as sliced inverse regression, sliced average variance estimation, projection pursuit regression, etc. Sliced inverse regression method can effectively deal with non-normal high-dimensional data, which is simple and easy to operate. The basic idea of sliced inverse regression method is: first through inverse regression to project high dimensional data to low dimensional space finding structure or projection which can reflect the characteristics of high dimensional data, thus extract active components of high-dimensional data and do further regression analysis. Compared with other dimensionality reduction methods, Sliced inverse regression method is more likely to promote and applicate in practical problems. This article not only uses the SIR dimension reduction method analyzes the problem of grain production of Chongqing, but also uses SIR dimension reduction method to study China’s commercial housing price from 2001 to 2014.After utilizing the method of SIR to make the high-dimensional data’s dimension reduction, we need the dimensionality reduction variables to make regression analysis. Traditional linear regression analysis can only fit linear relationships, but there are frequently a variety of non-linear relationships between the actual data. In order to more accurately investigate the actual data’s real relationships, we use semi-parametric additive models to fit the data which contained the information in the linear and nonlinear relationships.Semi-parametric additive model account the advantages of parametric and non-parametric model. The model is not only flexible, but also easily explain. The model is a theory which is a developed rapidly semiparametric model in recent years, but which in the application of the real problem is not enough, workers need to make data analysis for further researches. Therefore, this article used semiparametric additive regression implied in the Chinese commercial housing prices are particularly discussed in linear and nonlinear relations.