Locally minimax efficiency of nonparametric density estimators for \(\chi^2\)-type losses
The asymptotic expression of the locally minimax risk with weighted \(L_2\) losses is found. It is shown that in the case of \(\chi^2\)-type losses the expression is independent of the center of contracting neighborhoods. A locally minimax estimator for the \(\chi^2\)-type losses is constructed.
scientific article; zbMATH DE number 1542644