In the regression problem, we consider the problem of estimating the variance function by the means of aggregation methods. We focus on two particular aggregation setting: Model Selection aggregation (MS) and Convex aggregation (C) where the goal is to select the best candidate and to build the best convex combination of candidates respectively among a collection of candidates. In both cases, the construction of the estimator relies on a two-step procedure and requires two independent samples. The first step exploits the first sample to build the candidate estimators for the variance function by the residual-based method and then the second dataset is used to perform the aggregation step. We show the consistency of the proposed method with respect to the L 2error both for MS and C aggregations. We evaluate the performance of these two methods in the heteroscedastic model and illustrate their interest in the regression problem with reject option.

翻译：在回归问题中,我们考虑通过汇总方法估计差异函数的问题。我们侧重于两个特定的汇总设置:模型甄选汇总(MS)和Convex汇总(C),目标是分别选择最佳候选人和在候选人集中建立最佳候选人组合;在这两种情况下,估算器的构建都依靠两步程序,需要两个独立的样本。第一步利用第一个样本,用残余法构建候选人差异函数估计器,然后用第二个数据集来实施汇总步骤。我们显示了拟议方法在MS和C群中对于L2eror的一致性。我们用拒绝选项来评估这两个方法在超峰模型中的性能,并表明他们对回归问题的兴趣。