我院在读博士生彭镜夫在《Journal of Econometrics》发表论文。该研究主要在嵌套模型框架下，对模型平均和模型选择的最优风险进行比较，从而说明模型平均方法在回归函数估计上相较于模型选择的优势。
论文题目
On improvability of model selection by model averaging
文章摘要
In regression, model averaging (MA) provides an alternative to model selection (MS), and asymptotic efficiency theories have been derived for both MS and MA. Basically, under sensible conditions, MS asymptotically achieves the smallest estimation loss/risk among the candidate models, and MA does so among averaged estimators from the models with convex weights. Clearly, MA can beat MS by any extent in rate of convergence when all the candidate models have large biases that can be canceled out by a MA scheme. To our knowledge, however, a foundational issue has not been addressed in the literature. That is, when there is no advantage of reducing approximation error, does MA offer any significant improvement over MS in regression estimation? In this paper, we answer this question in a nested model setting that has been often used in the frequentist MA research area. A remarkable implication is that the much celebrated asymptotic efficiency of MS (e.g., by AIC) does not necessarily justify MS as commonly interpreted as achieving the best possible performance. In a nutshell, the oracle model (i.e., the unknowable best model among all the candidates) can be significantly improved by MA under certain conditions. A simulation study supports the theoretical findings.
作者介绍
彭镜夫，中国人民大学统计学院在读博士生，主要研究方向为模型平均，缺失数据分析等。
杨宇红，明尼苏达大学统计学院教授。主要研究方向为模型选择、多臂老虎机问题、预测、高维数据分析和机器学习。他在多个领域的顶级期刊上发表过文章，包括 Annals of Statistics、JASA、JRSSB、Biometrika、IEEE Transaction on Information Theory、Journal of Econometrics和Journal of Machine Leaning Research等。他是Institute of Mathematical Statistics的会员，并且曾获美国 NSF CAREER 奖。
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