Quantile Regression and Homogeneity Identification of a Semiparametric Panel Data Model
研究了一个含固定个体效应和非线性时间趋势的变指数系数面板数据模型，提出了基于样条逼近的估计方法和基于二元分割的同质性识别算法，并通过模拟和空气污染数据验证了方法的有效性。
In this article, we delve into the quantile regression and homogeneity detection of a varying index coefficient panel data model, which incorporates fixed individual effects and exhibits nonlinear time trends. Utilizing spline approximation, we obtain estimators for the trend functions, link functions, and index parameters, and subsequently establish the corresponding convergence rates and asymptotic normality. Observing that subjects within a group may share identical trend functions, we are motivated to further explore potential homogeneity in these trends. To this end, we propose a homogeneity identification algorithm based on binary segmentation. For the determination of the thresholding parameter in homogeneity identification, we propose a generalized Bayesian information criterion, following the approach outlined in Chen (2019). Furthermore, we introduce a penalized method to discern the constant and linear structures within the nonparametric functions of our model. By leveraging grouped observations, we achieve more efficient estimation and improve the asymptotic properties of the estimators. To demonstrate the finite sample performance of our proposed approach, we conduct simulation studies and apply our methodology to a real-world dataset comprising Air Pollution Data and Integrated Surface Data (APD&ISD).