Robust Regression And Variable Selection And Its Demonstration Based On The Nonconvex Penalty Likelihood Method

Linear regression model is widely used.The most classical method to estimate regression coefficient is least squares(OLS),which finds the best parameter estimate by minimizing the sum of squares.Although the process is easy to understand,the linear regression model collapses when severe outliers are present in the data.Moreover,when there are multiple explanatory variables in the data,the number of explanatory variables introduced has a great impact on the accuracy of model prediction accuracy.Therefore,the robust parameter estimation and variable selection of linear regression models are of great research importance.This paper introduces a mean drift parameter in a linear regression model and proposes a robust regression method based on the nonconvex penalized likelihood method.At the same time,an iteration-based algorithm is designed to estimate the mean drift parameters to identify outliers in the data and then calculate the robust parameter estimates of the linear regression model.Finally,the standard error of the regression coefficients was obtained using the bootstrap method,and robust interval estimates were obtained.The idea can also be applied to the variable selection study of linear regression,penalizing the regression parameters by the nonconvex penalty likelihood function and sparse the regression parameters to pick out the more important explanatory variables.The structure of this article is as follows: Chapter 1 introduces the development process and research results of domestic and foreign scholars in steady regression and variable selection,Non-convex penalty methods are found to be less studied in both areas,It shows that the topic is innovative;Chapter 2 presents least squares,outliers,and several common robust regression methods,Also describes the definition of the penalty likelihood function and several commonly used penalty functions;The third chapter describes the robust point estimation and interval estimation solving process based on the nonconvex penalty function and the bootstrap method;Chapter 4 introduces several commonly used variable selection methods and robust variable selection methods based on non-convex penalty functions,The definition and algorithm of the penalty likelihood function are also given;Chapter V,Through two simulation experiments,To verify the robustness and high efficiency of the nonconvex penalized regression methods;Chapter 6 provides a summary of the full text.