| Abstract: | Summary This paper discusses, with measure-theoretical rigor, some basic aspects of the theory of separate inference. To analyze densities
of marginal and conditional submodels, certain operators are introduced. First a general concept of decomposition of a model
is proposed, and the corresponding factorization of densities of the model is established. Next it is shown that the property
of smoothness of a family of densities is retained in the operation of conditioning, and therefore it yields the differentiability
of the conditional expectation of a real-valued statistic in a certain sense. On the basis of this result, two measures of
the effectiveness of a submodel in separate inference are investigated.
The Institute of Statistical Mathematics |
