Improved two-stage model averaging for high-dimensional linear regression, with application to Riboflavin data analysis.

BACKGROUND

Model averaging has attracted increasing attention in recent years for the analysis of high-dimensional data. By weighting several competing statistical models suitably, model averaging attempts to achieve stable and improved prediction. In this paper, we develop a two-stage model averaging procedure to enhance accuracy and stability in prediction for high-dimensional linear regression. First we employ a high-dimensional variable selection method such as LASSO to screen redundant predictors and construct a class of candidate models, then we apply the jackknife cross-validation to optimize model weights for averaging.

RESULTS

In simulation studies, the proposed technique outperforms commonly used alternative methods under high-dimensional regression setting, in terms of minimizing the mean of the squared prediction error. We apply the proposed method to a riboflavin data, the result show that such method is quite efficient in forecasting the riboflavin production rate, when there are thousands of genes and only tens of subjects.

CONCLUSIONS

Compared with a recent high-dimensional model averaging procedure (Ando and Li in J Am Stat Assoc 109:254-65, 2014), the proposed approach enjoys three appealing features thus has better predictive performance: (1) More suitable methods are applied for model constructing and weighting. (2) Computational flexibility is retained since each candidate model and its corresponding weight are determined in the low-dimensional setting and the quadratic programming is utilized in the cross-validation. (3) Model selection and averaging are combined in the procedure thus it makes full use of the strengths of both techniques. As a consequence, the proposed method can achieve stable and accurate predictions in high-dimensional linear models, and can greatly help practical researchers analyze genetic data in medical research.