Methodology for the invariant estimation of a continuous distribution function
Invariant estimation of a continuous distribution function with the weighted quadratic loss function and a sample of a fixed size is considered. Let N be the class of invariant estimators. Imposing some additional conditions on estimators, a sequence of more general invariance problems with classes \(U_ m\), \(m=1,2,..\). of invariant estimators is defined. Approximation of estimators from N by estimators from \(U_ m\) is established. Results like ``d is admissible in N iff it is admissible in \(U_ 1\)'' are presented. The problem of minimaxity of estimators is discussed.
scientific article; zbMATH DE number 4145141