Expectile and M-quantile regression for panel data

Linear fixed effect models are a general way to fit panel or longitudinal data with a distinct intercept for each unit. Based on expectile and M-quantile approaches, we propose alternative regression estimation methods to estimate the parameters of linear fixed effect models. The estimation functions are penalized by the least absolute shrinkage and selection operator to reduce the dimensionality of the data. Some asymptotic properties of the estimators are established, and finite sample size investigations are conducted to verify the empirical performances of the estimation methods. The computational implementations of the procedures are discussed, and real economic panel data from the Organisation for Economic Cooperation and Development are analyzed to show the usefulness of the methods in a practical problem.