We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax rate of aggregation is of order log(M), where M is the number of estimators to aggregate. It is proved that for affine estimators, the minimax rate of aggregat...

This article presents the results of an empirical experiment designed to gain insight into what is the effect of the minimax algorithm on the evaluation function. The experiment’s simulations were performed upon the KRK chess endgame. Our results show that dependencies between evaluations of sibling nodes in a game tree and an abundance of possibilities to commit blunders present in the KRK end...

In this paper we propose a new derivative-free algorithm for linearly constrained finite minimax problems. Due to the nonsmoothness of this class of problems, standard derivative-free algorithms can only locate points which satisfy weak necessary optimality conditions. In this work we define a new derivative-free algorithm which is globally convergent toward standard stationary points of the fi...

We consider the problem of testing hypotheses on the copula density from n bidimensional observations. We wish to test the null hypothesis characterized by a parametric class against a composite nonparametric alternative. Each density under the alternative is separated in the L2-norm from any density lying in the null hypothesis. The copula densities under consideration are supposed to belong t...

PURPOSE To compare the clinical benefit of robust optimized Intensity Modulated Proton Therapy (minimax IMPT) with current photon Intensity Modulated Radiation Therapy (IMRT) and PTV-based IMPT for head and neck cancer (HNC) patients. The clinical benefit is quantified in terms of both Normal Tissue Complication Probability (NTCP) and target coverage in the case of setup and range errors. MET...

We consider the problem of estimating, in the presence of model uncertainties, a random vector x that is observed through a linear transformation H and corrupted by additive noise. We first assume that both the covariance of x and the transformation H are not completely specified, and develop the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible covaria...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.