Analysis Of The Linear Regression Modeling For High-dimensional Data

Regression analysis is one of the most important part in mathematical statis-tics all the time. In recent years,the technique of regression analysis is wildlyused in many fields such as industry, agriculture, hydrometeorology, economics,health and so on. With the development of modern science, the technology ofdata collecting has improved a lot. However, for certain structure of data, theclassic regression methods are not applicable so that more favorable methods arerequired.While assessing the pros and cons of the linear regression models, a fairlyimportant part is the fitness for actual situation under the model.There are fourmain efects in the model to be considered.That is the accuracy of prediction,thereality of variable selection,the speed of computing while convergence and thestability of the model.This paper begins with some classic linear regression modelssuch as All-subset regression,stepwise regression,ridge regression,Lasso regressionand Least angle regression.And then it thoroughly discusses the properties andfeatures as parameter estimation and variable selection of the above models.Onthe basis of classic linear models,this paper elaborates diferent improved modelsin detail that are applicable for diferent kinds of data structures such as FusedLasso,Elastic net regression and so on which have great advantage for classicmodels.At last this paper uses the simulated data and the Consumer Price Indexdata to model.Combing with the current economic situation, this paper interpretsthe results of the tests and finally achieves favorable efects.