近日，据Journal of Econometrics官网显示，北京大学光华管理学院涂云东教授与其指导的在读博士生孙喆合作完成的论文“MCA: High-Dimensional Modal Component Analysis towards the Mode”（聚焦众数的高维成分分析），已在计量经济学国际顶刊Journal of Econometrics 发表。

# 论文简介 #

Title：

MCA: High-Dimensional Modal Component Analysis towards the Mode

Author：

Zhe Sun, Yundong Tu 

Abstract：

 The modal factor model represents a novel statistical framework for dimension reduction in high dimensional panel data analysis. It is specifically designed to capture modal factors which exert a significant influence on the conditional mode of the distribution of the observables. Statistical inference for this model is developed based on a newly proposed modal component analysis, where modal factors and their corresponding loadings are estimated through maximizing a kernel-type objective function. Two computationally efficient and easy-to-implement algorithms—minorization-maximization and alternating maximization—are devised for the numerical computation of these estimators. Furthermore, two model selection criteria are proposed to determine the optimal number of modal factors. Under mild regularity conditions that accommodate both cross-sectional and time-series dependence, the asymptotic properties of the proposed estimators are established. Additionally, the limiting distributions of parameter estimators and forecasts derived from factor-augmented regressions incorporating estimated modal factors are rigorously derived. Simulation studies demonstrate that the proposed estimators exhibit favorable finite-sample performance, even in the presence of heavy-tailed, skewed, multimodal, and heteroskedastic error distributions. Finally, an application to inflation and industrial production index forecasting validates the practical merits and superior predictive power of modal factors in real-world macroeconomic scenarios.

标题： 

聚焦众数的高维成分分析

中文摘要：

模态因子模型是一种新颖的统计框架，旨在对高维面板数据进行降维分析。该模型专门用于捕捉对观测值条件众数具有显著影响的模态因子。基于新提出的模态成分分析，通过最大化核型目标函数来估计模态因子及其对应的载荷，并据此建立统计推断。为方便数值计算，设计了两种计算高效且易于实现的算法——最小化-最大化算法和交替最大化算法。此外，提出了两个模型选择准则以确定最优模态因子个数。在允许横截面和时间序列相依性的温和正则条件下，建立了所提估计量的渐近性质。同时，严格推导了包含估计模态因子的因子增强回归中参数估计量和预测值的极限分布。模拟研究表明，即便在误差分布呈现重尾、偏态、多峰和异方差的情况下，所提估计量仍具有优良的有限样本表现。最后，应用于通货膨胀和工业生产指数预测的实例验证了模态因子在实际宏观经济场景中的实用价值和优越的预测能力。