Random coefficient regressions: parametric goodness of fit tests

Abstract

Random coefficient regression models have been applied in different fields during recent years and they are a unifying frame for many statistical models. Recently, Beran and Hall (1992) opened the question of the nonparametric study of the distribution of the coefficients. Nonparametric goodness of fit tests were considered in Delicado and Romo (1994.). In this paper we propose statistics for parametric goodness of fit tests and we obtain their asymptotic distributions. Moreover, we construct bootstrap approximations to these distributions, proving their validity. Finally, a simulation study illustrates our results.