Efficient pseudo-Gaussian and rank-based detection of random regression coefficients

Random coefficient regression models are the regression counterparts of the classical random effects models in Analysis of Variance and panel data analysis. While several heuristic methods have been proposed for the detection of such random regression coefficients, little is known on their optimality properties. Based on a nonstandard ULAN property, we are proposing locally asymptotically optimal (in the Hajek-Le Cam sense) parametric, pseudo-Gaussian, and rank-based procedures for this problem. The asymptotic relative efficiencies (with respect to the pseudo-Gaussian procedure) of rank-based tests turn out to be quite high under heavy-tailed and skewed densities, demonstrating the importance of a careful choice of scores. Simulations reveal the excellent finite-sample performances of a class of rank-based procedures based on data-driven scores.