Analysis of marginal and conditional density functions for separate inference (Q1090022)

In the inference on parameters of interest from a part of the original model and data, the author considers a decomposition of the model into submodels and their efficacies. He discusses the factorization of densities of a model, the smoothness of a family of conditional densities, the differentiability of the conditional expectation of a statistic, and the conditional efficacy. The averaging operators introduced by \textit{E. J. G. Pitman}, Some basic theory for statistical inference. Chapman and Hall (1979; Zbl 0442.62002), and their properties are also discussed.