Bicluster Analysis Of Heterogeneous Panel Data Via M-Estimation

Panel data models can fully utilize both cross-sectional and time-series information in panel data,and are widely used in fields such as economics and finance.However,traditional panel data models often assume that the regression coefficients do not vary with individuals and time,which is too rigid an assumption.In many applications,heterogeneity in both the individual and time dimensions often coexists,i.e.,different individuals or different time periods have different regression coefficients.Reasonable modeling and estimation of these potential heterogeneity factors can make the model adapt to more complex scenarios.In this paper,we study a two-dimensional heterogeneous panel data model with a block structure that can simultaneously model the heterogeneity in the individual and time dimensions.The model’s regression coefficients have both an individualgroup structure and a time-breakpoint structure,where the individual-group structure can change at breakpoints,and the time-breakpoint structure can exhibit differences across different groups.The regression coefficients are the same within the same subblock,and show heterogeneity across different sub-blocks.This block structure is flexible,and the homogeneous panel data model,the panel data model with group structure,and the panel data model with breakpoint structure can all be viewed as special cases of it.We propose a robust clustering method based on M-estimation and double concave fused penalties,which can simultaneously recover the unknown block structure and estimate the regression coefficients.The M-estimator exhibits robustness to heavy-tailed distributions and outliers,while the double concave fused penalty can automatically identify potential block structures.We develop an effective algorithm rooted in local quadratic approximation to optimize the objective function,which has higher computational efficiency compared with ADMM algorithm.In addition,we establish the asymptotic convergence property of the Oracle estimator and prove that the proposed estimator can recover the latent block structure with probability approaching 1.Simulation experiments on multiple data sets and an application on a real data set show that the estimator proposed in this paper has excellent performance in finite sample situations.When the data distribution is heavy-tailed,models based on L1 loss and Huber loss functions can achieve more accurate results than those based on L2 loss functions.