ABSTRACT
The exponential family model is another general model class. Its prominence in the theory of inference can be explained, first, by the useful analytical properties it possesses, and second, by the fact that a very large number of commonly used statistical models belong to this class. An introduction to the regular family precedes introduction of the exponential family. The regular family is essentially defined by a number of technical assumptions which permit a definition, or at least a useful interpretation, of Fisher information. A discussion of statistical models leads to the problem of data reduction. Equivariant statistics preserve the effect of a transformation, and are usually used as estimators. In contrast, invariant statistics do not change value when the data is transformed. Both play an important and complementary role for invariant families.
