Consider the location-scale regression model Y = m(X)+o(X), where the error e is independent of the covariate X, and m and o are smooth but unknown functions.We construct tests for the validity of this model and show that the asymptotic limits of the proposed test statistics are distribution...

Consider the nonparametric regression model Y = m(X)+e, where the function m is smooth, but unknown. We construct tests for the independence of e and X, based on n independent copies of (X; Y). The testing procedures are based on differences of neighboring Y's. We establish asymptotic results...

When simultaneously monitoring two possibly dependent, positive risks one is often interested in quantile regions with very small probability p. These extreme quantile regions contain hardly or no data and therefore statistical inference is difficult. In particular when we want to protect...