摘要翻译：
本文建立了中心极限定理，并提出了如何在因子模型中进行有效的推理。我们考虑这样一个环境，其中许多县/地区/资产在许多时间段内被观察，并且当一个全局参数的估计包括对每个实体分别估计的异构微观参数的横截面的聚合时。中心极限定理适用于涉及横截面和时间序列聚集的量，以及时间聚集误差中的二次型。本文研究了渐近方差的一致估计条件，并对不能一致估计的情况提出了bootstrap方案。一个小的仿真研究说明了渐近和自举过程的性能。这些结果对于在与因子模型相关的两步估计过程中以及在其他相关的上下文中做出推论是有用的。我们的处理避免了横截面依赖的结构建模，但强加了时间序列独立性。
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英文标题：
《Limit Theorems for Factor Models》
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作者：
Stanislav Anatolyev and Anna Mikusheva
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最新提交年份：
2020
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous micro-parameters estimated separately for each entity. The central limit theorem applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. The paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.
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PDF链接：
https://arxiv.org/pdf/1807.06338