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...

Classical stochastic programming has already been used with large scale LP models for long-term analysis of energy-environment systems. We propose a Minimax Regret formulation suitable for large scale linear programming models. It has been experimentally verified that the minimax regret strategy depends only on the extremal scenarios and not on the intermediate ones, thus making the approach co...

We present a topological minimax theorem (Theorem 2.2). The topological assumptions on the spaces involved are somewhat weaker than those usually found in the literature. Even when reinterpreted in the convex setting of topological vector spaces, our theorem yields nonnegligible improvements, for example, of the Passy–Prisman theorem and consequently of the Sion theorem, contrary to most result...

We consider the estimation of regression coefficients in a high-dimensional linear model. A lower bound of the minimax `q risk is provided for regression coefficients in `r balls, along with a minimax lower bound for the tail of the `q loss. Under certain conditions on the design matrix and penalty level, we prove that these minimax convergence rates are attained by both the Lasso and Dantzig e...