随机子集平均法
Random Subset Averaging
AI总结：
针对多协变量尤其是强相关情况提出随机子集平均法（RSA），通过二项随机子集策略构建候选模型，经两轮加权聚合预测，调参用交叉验证，证明其渐近最优及在正交设计下有限样本风险界更低，模拟和实证显示性能优越。
摘要：
我们提出一种新的集成预测方法，随机子集平均法（RSA），专为具有许多协变量的设置量身定制，特别是在存在强相关性的情况下。RSA通过二项式随机子集策略构建候选模型，并通过两轮加权方案聚合其预测，从而产生类似于两层神经网络的结构。所有调优参数均通过交叉验证选择，无需事先了解协变量相关性。我们在一般条件下建立了RSA的渐近最优性，允许第一轮权重依赖于数据，并证明RSA在正交设计下实现了更低的有限样本风险界。模拟研究表明，RSA在广泛的样本大小、维度设置、稀疏水平和相关结构中始终提供卓越且稳定的预测性能，优于传统的模型选择和集成学习方法。对金融回报预测的实证应用进一步说明了其实际效用。
英文摘要：
We propose a new ensemble prediction method, Random Subset Averaging (RSA), tailored for settings with many covariates, particularly in the presence of strong correlations. RSA constructs candidate models via binomial random subset strategy and aggregates their predictions through a two-round weighting scheme, resulting in a structure analogous to a two-layer neural network. All tuning parameters are selected via cross-validation, requiring no prior knowledge of covariate relevance. We establish the asymptotic optimality of RSA under general conditions, allowing the first-round weights to be data-dependent, and demonstrate that RSA achieves a lower finite-sample risk bound under orthogonal design. Simulation studies demonstrate that RSA consistently delivers superior and stable predictive performance across a wide range of sample sizes, dimensional settings, sparsity levels and correlation structures, outperforming conventional model selection and ensemble learning methods. An empirical application to financial return forecasting further illustrates its practical utility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
