Despite their importance, optimal designs for quantile regression models have not been developed so far. In this article, we investigate the <italic>D</italic>-optimal design problem for nonlinear quantile regression analysis. We provide a necessary condition to check the optimality of a given design and use it...

In the common nonparametric regression model, we consider the problem of testing the hypothesis that the coefficient of the scale and location function is constant. The test is based on a comparison of the standardized (by a local linear estimate of the scale function) observations with their...