Functional Panel Quantile Regression Models with Group Structured Fixed Effect Functions
Panel data analysis and functional data analysis are both popular research in many fields,such as statistics and econometrics.As practical applications become more complex,the types of data become more and more diverse,and the homogeneity and heterogeneity of data often exist simultaneously.Thus,it is very necessary to identify the homogeneity and heterogeneity of data before making correct and effective statistical inferences.In this paper,we propose functional panel quantile regression models with unknown group fixed effect functions.The computation of quantile re-gression can be extremely challenging due to the fact that panel data are a combination of time series data and cross-sectional data,as well as the infinite-dimensional feature of functional data.We adopt the newly proposed convolution method to smooth the objective function to deal with the computational complexity associated with such large samples and high-dimensional data.We combine the Bayesian information cri-terion and the hierarchical agglomerative clustering algorithm to identify potential group structures.Based on the identified group structure information,we further pro-pose an efficient method to estimate the bivariate time-varying coefficient function.In this paper,we also prove the consistency of the group identification methods and the asymptotic normality of the corresponding estimators.And through several numerical simulation results and analyses of the household electricity consumption data and Gini coefficient data of 87 counties in Jiangxi Province,we illustrate the rationality of the proposed model and the validity of the estimation procedure.
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