Nonparametric Quantile Regression for Homogeneity Pursuit in Panel Data Models

Many panel data have the latent subgroup effect on individuals, and it is important to correctly identify these groups since the efficiency of resulting estimators can be improved significantly by pooling the information of individuals within each group. However, the currently assumed parametric and semiparametric relationship between the response and predictors may be misspecified, which leads to a wrong grouping result, and the nonparametric approach hence can be considered to avoid such mistakes. Moreover, the response may depend on predictors in different ways at various quantile levels, and the corresponding grouping structure may also vary. To tackle these problems, this paper proposes a nonparametric quantile regression method for homogeneity pursuit, and a pairwise fused penalty is used to automatically select the number of groups. The asymptotic properties are established, and an ADMM algorithm is also developed. The finite sample performance is evaluated by simulation experiments, and the usefulness of the proposed methodology is further illustrated by an empirical example.