Quantile factor models (QFM) represent a new class of factor models for high‐dimensional panel data. Unlike approximate factor models (AFM), which only extract mean factors, QFM also allow unobserved factors to shift other relevant parts of the distributions of observables. We propose a quantile regression approach, labeled Quantile Factor Analysis (QFA), to consistently estimate all the quantile‐dependent factors and loadings. Their asymptotic distributions are established using a kernel‐smoothed version of the QFA estimators. Two consistent model selection criteria, based on information criteria and rank minimization, are developed to determine the number of factors at each quantile. QFA estimation remains valid even when the idiosyncratic errors exhibit heavy‐tailed distributions. An empirical application illustrates the usefulness of QFA by highlighting the role of extra factors in the forecasts of U.S. GDP growth and inflation rates using a large set of predictors.

中文翻译：

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分位数因子模型

分位数因子模型（QFM）代表了用于高维面板数据的一类新的因子模型。与仅提取均值因子的近似因子模型（AFM）不同，QFM还允许未观测因子转移可观测变量分布的其他相关部分。我们提出了一种称为分位数因子分析（QFA）的分位数回归方法，以一致地估计所有与分位数有关的因子和负载。它们的渐近分布是使用QFA估计器的内核平滑版本建立的。根据信息标准和等级最小化，开发了两个一致的模型选择标准，以确定每个分位数的因素数量。即使特质误差表现出重尾分布，QFA估计仍然有效。