Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in different fields and they constitute a unifying setup for many statistical problems. The nonparametric study of this model started with Beran and Hall (1992) and it has become a fruitful framework. In this paper we propose and study statistics for testing a basic hypothesis concerning this model: the constancy of coefficients. The asymptotic behavior of the statistics is investigated and bootstrap approximations are used in order to determine the critical values of the test statistics. A simulation study illustrates the performance of the proposals.