Tuning Parameter Selection Based On Blocked 3×2 Cross-validation In High Dimensional Regression

In practical application fields, such as the biological information, image processing, financial management, we often meet high-dimensional data. But even in the simplest lin-ear regression model, the traditional low dimensional data processing methods have become helpless.when facing such data, how to process those high-dimensional data becomes a problem need to solve. One direct method of dealing with high dimensional data is reducing the variable dimension to within the sample number, then using the conventional methods for processing. In recent years, in the high-dimensional regression variable selection, regu-larization variable selection methods have been proposed and obtained some good results, such as LASSO, SCAD and MCP. However, those methods are dependenting on the tuning parameters’s selection (regularization parameter). Therefore, providing a proper tuning pa-rameter selection method to ensure it can consistently identify the true model is very key to model selection.In the traditional statistical learning method based on cross-validation is widely used in the selection of tuning parameters, but it also shows a bad performance when facing high-dimensional data. Based on the advantages of recently proposing blocked 3x2 cross validation in computational complexity, model selection and performance comparison, we consider apply it to tuning parameter selection of regularization variable selection method . in high-dimensional regression.First of all, this paper proves that under certain conditions, based on blocked 3x2 cross validation sleceted tuning parameter can ensure regularization variable selection method can identify the true model in the high-dimensional regression, namely the blocked 3x2 cross-validation has the consistency of tuning parameter selection. Next, we compare our method with the Akaike information criterion, Bayes information criterion, Extened Bayes information criterion, High dimension Bayes information criterion, Hold-Out method,5 fold cross-validation,10 fold cross-validation in simulation experiment of linear regression and logistic regression. Finally, by comparing the various methods of training error and testing error and computational complexity, we can obtain blocked 3x2 cross validation method is better than other methods or has comparable performance in the advertisement data.