近年来，由于频率模型平均方法能够提供更好的估计和预测，所以引起了研究学者的普遍关注。相较于传统的模型选择方法，模型平均考虑了各个模型的不确定性，把来自不同模型的估计和预测加权起来对总体进行推断。这种平均的思想可以避免选择一个较差的模型，因此有望降低估计风险。本项目拟探究频率模型平均方法在理论和实践中亟待解决的若干问题，具体包括以下三点：一是分别研究区间值数据、长度偏差数据和处理效应模型下的模型平均估计，并证明这些特殊数据类型下权重选择准则的渐近最优性；二是理论推导出非“局部误设定”假设下常见模型平均估计量(S-AIC, S-BIC, Mallows' 和Jackknife)的渐近分布；三是通过模型平均方法对一些中国大陆和香港经济指数进行修正并做成实际案例。另外，为了方便实际工作者应用模型平均方法，本项目也计划开发频率模型平均方法的R语言程序包。

The widespread findings that model averaging can lead to better estimators have attracted a great deal of attention in recent years. Compared with traditional model selection methods, model averaging allows for model uncertainty and weights the estimates or predictions from different models to infer the population. Averaging shields against the choice of a very poor model, and thus holds promise for reducing estimation risk. The proposal contains three subprojects that seek to expand our knowledge of model averaging in areas that have been unexplored or insufficiently investigated. The first subproject develops model averaging methods under interval-value and length biased data, and considers model averaging for estimating “treatment effects”, a term commonly used to refer to the causal effects of a binary variable on an outcome variable of scientific or policy interest. Our second subproject investigates post-model averaging inference by deriving the distributions of some commonly used model average estimators (S-AIC, S-BIC, Mallows' and Jackknife). Our work will consider a fixed parameter setup, and the results developed will have broader applicability than those obtained under local misspecification. The last part of the project considers using model averaging to improve the methodology associated with the construction of several highly popular Chinese and Hong Kong economic indices, including the Centa-City Index, the Chinese Consumer Confidence Index and the Consumer Satisfaction Index. In addition, we will develop an R language package for the proposed methods.