Smoothed Quantile Regression for Panel Data Models with a Mixed Group Structure

李海奇，厦门大学经济学博士，现为湖南大学金融与统计学院教授、博士生导师，副院长。曾任美国康奈尔大学经济学系访问学者。目前研究方向为金融计量经济学、金融工程、数据科学等，研究成果发表于经济学国际顶尖和权威期刊以及中文重点期刊，如Journal of Econometrics（3篇），Econometric Theory, Econometric Reviews（2篇），Journal of Futures Markets，《数量经济技术经济研究》《统计研究》《中国管理科学》《计量经济学报》等。曾主持国家自然科学基金项目、教育部人文社科规划基金项目、湖南省自然科学基金杰出青年项目等多项国家和省部级科研项目。曾获得湖南省优秀硕士学位论文指导教师、湖南大学科研标兵、湖南大学优秀教师、湖南大学财经教育基金优秀青年教师奖、湖南大学本科毕业论文优秀指导教师等荣誉或奖励。

This study develops a novel framework for estimating common parameters and latent group heterogeneity in panel quantile regression models, where a subset of coefficients share common values across unknown groups. To address challenges from non-differentiable objective functions, we propose a Smoothed Panel Quantile Regression with a Mixed Group Structure (SPQR-MGS) and introduce an innovative penalized K-means method for simultaneous group identification and parameter estimation. Theoretically, this approach consistently recovers the true group structure. While the post-selection estimator exhibits asymptotic normality, we uncover  substantial asymptotic bias and consequently develop two bias-correction approaches---analytical and half-panel jackknife---that yield asymptotically unbiased, zero-mean normal distributions. We further extend the methodology to accommodate multi-dimensional group structures. Monte Carlo simulations confirm superior finite-sample performance against benchmark methods. An empirical application to stock return predictability validates the practical utility of our SPQR-MGS framework and penalized K-means in financial econometrics.