The Application Of Lasso And Its Related Methods In Multiple Linear Regression Model

Model and variable selection is one of the most important problems in modern statistics. My paper compares the optimal property of Lasso and other related methods which solve the variable selection problem in ordinary linear regression model, and give a new algorithm, random simulation algorithm, which can solve the Lasso. This new algorithm can work similarly with LAR algorithm. Multiple linear regression model is used more widely than ordinary linear regression model, but its variable selection problem is studied rarely. So my paper study the model selection problem in multiple linear regression model by taking advantage of the idea of Lasso, and give four methods of variable selection in multiple linear regression model, and solve them by use of random simulation algorithm. We also analyze a real diabetes data and a random multi-linear data, for showing the ways of variable selection.My paper introduces the research results of Lasso in ordinary linear regression model about variable selection in the first part. Then the second part describes the main theory of Lasso. The third part describes two algorithms about solving Lasso problem and gives a new one called random simulation algorithm. And we use a real case to prove its optimal property. The forth part introduces some related methods about Lasso. The fifth part we solve the multiple linear regression model by the idea of Lasso. And we use a random multi-linear data to make it true.