Conference Agenda

There is a great variety of statistical models expressing relations between response variables of interest and explanatory variables, ranging from classical conditional mean regression to fully distributional regression models. We are particularly interested in expressing regression models by means of copulas which are a valuable tool to separate marginal distributions and dependencies. New goodness-of-fit tests and new measures of deviation can be developed based on such copula representations. These tests are desirable since regression models often impose parametric or semiparametric assumptions to overcome the curse of dimensionality, running a risk of misspecification. We present a new goodness-of-fit test for the classical mean regression model. More importantly, we also introduce a new measure of deviation between the true regression function and the imposed parametric assumption. By self-normalization, we develop pivotal inference for this measure including tests for relevant hypotheses. These inference tools are illustrated via simulated and empirical data.