Group structure detection for a high‐dimensional panel data model

Abstract

This article investigates latent group structures in a high‐dimensional panel data model. It is assumed that subjects are classified into unobserved groups, where the fixed effects for each subject are the same within a group but heterogeneous across different groups. A penalized regression approach is proposed to identify latent group structures and significant covariates simultaneously. A new algorithm is proposed to optimize the objective function. When the sample size goes to infinity, it is shown that the proposed estimator recovers latent group structures and important covariates with probability approaching one. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies and illustrated using a real dataset.

Bicluster Analysis of Heterogeneous Panel Data via M-Estimation

“…To achieve both automatic recovery of the parameter structure and unbiased or nearly unbiased estimation of coefficients, concave fused penalty functions have been proposed, such as the smoothly clipped absolute deviation (SCAD) [15] and the minimax concave penalty (MCP) [16]. In this paper, following the approach of Wang and Zhu [3], Ma and Huang [17], Wang et al [18], we use the SCAD penalty function with a tuning parameter λ,…”

“…Remark 1. Assumption (A1) is a regularization assumption on the design matrix, where the minimum and maximum eigenvalues of (NT) −1 Z Z are bounded by constants, which is a common assumption in heterogeneity panel data analysis based on concave fused penalties; see Ma and Huang [17], Ma et al [22], Wang and Zhu [3], etc. Assumption (A2) allows the real coefficients dimension L 0 P to increase with the sample size NT but at a slower rate.…”

“…This method is based on a penalized objective function inspired by the fused Lasso method introduced by Tibshirani et al [2]. Wang and Zhu [3] study high-dimensional panel data models using a concave fused penalty method for both subgroup identification and variable selection and proved the asymptotic properties of the proposed estimator under specific regularity conditions. To capture the heterogeneity that may exist over time, structural breaks are often assumed.…”