Suppose we have i.i.d. observations with a distribution equal to the convolution of an unknown distribution function F and a known distribution function K. We derive local minimax lower bounds for the problem of estimating F , its density f and its derivatives at a xed point x 0. Contrary to a previous local minimax bound in Van Es (1998) only smooth perturbations are considered. The local boun...

Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or minG. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.

This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...

AbstractIn this paper we formulate Stein–minimax type estimators and compare the performance properties with other estimators in case of mean value predictions. When the model is estimated by ordinary least squares it has been observed that least squares predicted is unbiased while minimax and Stein-minimax predictors are biased. The superiority conditions of the estimators have been derived by...