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摘要翻译：
最近的计量经济学文献通过给每个截面单位分配一维离散的潜在类型来模型面板数据中未观察到的截面异质性。这些模型已经被证明允许用回归聚类方法进行估计和推断。本文的动机是发现，在文献中研究的聚类异质性模型可能会严重错误地描述，即使面板具有显著的离散截面结构。为了解决这个问题，我们通过允许每个单元具有多个不完全相关的潜在变量来描述其对不同协变量的响应类型，从而推广了以前对离散未观察异质性的方法。我们给出了模型的k-means型估计量的推断结果，并提出了联合选择每个潜在变量的数目簇的信息准则。蒙特卡罗模拟证实了我们的理论结果，并给出了有限样本估计和模型选择的直观性。我们也贡献了超过特定数目的聚类理论，并导出了这种情况下新的收敛速度。我们的结果表明，当聚类数目过大时，在K-均值型估计器中可能会出现严重的过拟合。
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英文标题：
《Blocked Clusterwise Regression》
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作者：
Max Cytrynbaum
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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：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference by regression clustering methods. This paper is motivated by the finding that the clustered heterogeneity models studied in this literature can be badly misspecified, even when the panel has significant discrete cross-sectional structure. To address this issue, we generalize previous approaches to discrete unobserved heterogeneity by allowing each unit to have multiple, imperfectly-correlated latent variables that describe its response-type to different covariates. We give inference results for a k-means style estimator of our model and develop information criteria to jointly select the number clusters for each latent variable. Monte Carlo simulations confirm our theoretical results and give intuition about the finite-sample performance of estimation and model selection. We also contribute to the theory of clustering with an over-specified number of clusters and derive new convergence rates for this setting. Our results suggest that over-fitting can be severe in k-means style estimators when the number of clusters is over-specified.
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PDF链接：
https://arxiv.org/pdf/2001.11130
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