Loss of information in the presence of nuisance parameters and partial sufficiency
The author considers a parametric model for a random variable X with a density p(x,\(\theta\),\(\Phi\)), where \(\theta\) is a vector-valued parameter of interest and \(\Phi\) a vector-valued nuisance parameter. He obtains relations between the total Fisher information on \(\theta\) and the Fisher information in a statistic S(X) whose distribution depends only on \(\theta\). Under the regularity conditions it is shown that if S(X) is weakly partially sufficient, it has no loss of information. He also considers the generalized Fisher information, and obtains similar results to the above. Some examples are given.
partial sufficiency in the complete sense
scientific article; zbMATH DE number 4215142
scientific article