On random translation models

We introduce a nonparametric location model and discuss its relations to the more familiar parametric location model and the mixture location model. The model can be characterized as a random translation model. Further characterizations are given by means of conditional distributions, by characteristic functions and by the local structure of the model in terms of the tangent cone. The relations between two different nonparametric location models can be made explicit. We consider especially the total variation distance and the deficiency. Consequences of these results for the statistical analysis of models of this type will be discussed in a subsequent paper.