This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels.

翻译：本文考虑具有个体效应的面板分位数回归中函数系数模型的估计问题，允许大面板观测数据存在横截面与时间相依性。通过在异质分位数回归模型中施加潜变量组结构，可显著减少需要估计的非参数函数系数数量。利用初步的局部线性分位数估计量获取个体特定函数系数后，采用经典凝聚聚类算法估计未知组结构，并提出易于实现的比率准则确定组数。证明所估计的组数与结构具有一致性。进一步引入分组后局部线性平滑方法估计组特定函数系数，推导出具有与文献可比标准化率的渐近正态分布理论。通过模拟研究验证所提方法与理论，并将其应用于英国地方政府辖区房价数据，揭示了不同分位点水平下的异质性结构差异。