当有很多候选模型并且不确定使用哪个模型时, 模型平均是一种值得采用的方法.} 相对于单个模型, 模型平均通常能够提高预测精度. 文章提出了高维泊松回归的模型平均方法, 证明了其最优性质, 并通过数值模拟发现该方法能够提高计数变量的预测精度. 同时, 考虑到高维数据下, 候选模型过多的问题, 文章也提出了一种新的模型筛选方法: 基于最小角回归 (LARS) 的LASSO (或ALASSO) 修正算法的模型筛选方法. 该种方法, 可以大大减少计算负担. 数值模拟也显示了该方法有很好的表现.

When there are many candidate models and people are uncertain which model to use, model averaging can be used. Comparing to using a single model, model averaging can improve the forecasting precision. In this paper, we propose a model averaging method for high dimensional Poisson regression model. The proposed model averaging is proved to enjoy an asymptotic optimality. Meanwhile, considering the issue that the candidate models are numerous under the high dimensional data, we propose a new method to select the candidate model set. This method is based on least angle regression (LARS)-LASSO (ALASSO) algorithm. It can reduce the number of the candidate models greatly, and effectively reduce the computation burden. Simulation results show that our model averaging improves finite sample performance over a range of estimators including the LASSO and ALASSO estimators.