Quantile Regression Under Equality Constraint With Factor Variable Selection

In many practical regression applications,we are faced with the fact that least square es-timators can not fully depict the relationship between variables.At this time,the emergence of quantile regression solves such problems.It can describe the characteristics of the distri-bution more comprehensively,thus get a comprehensive analysis,and the quantile regression coefficient estimation is more robust than the OLS regression coefficient estimation.In the statistical inference problem of almost all practical fields,there will be a predeter-mined condition for the given statistical model,especially in the fields of medicine,environ-mental science,economics and finance,these conditions are usually prior knowledge or theo-ries,which provide more information for statistical inference and make them more reasonable.Therefore,it is necessary to take the constraints into account when estimating parameters.In practice,in order to reduce the model bias,a large number of predictive variables will be selected in the model fitting,but the selection of unrelated variables will aggravate the difficulty of interpretation and reduce the accuracy of the prediction.Therefore,the selection of variables is particularly important.In many regression problems,in order to increase the flexibility of the model,an explanatory variable is made up of a set of variables.When there is only one variable in each group,group variables selection includes single variable selection.Therefore,identifying the important factor group has wider application scope.Based on this idea,we use adaptive sup-norm to do penalty function for group variable selection.The study of quantile regression is mainly based on three steps.First,we transform the objective function and combine the Lagrange multiplier method to give the asymptotic property of its estimation under constraints.The second we use the adaptive sup-norm as a penalty function for the selection of the group variables,first we give the consistency of the estimation,then we prove the sparsity,and finally we give the oracle property.Finally,a simulation study is given to show that the proposed estimation method is excellent and effective.