Game-playing programs usually evaluate moves by searching the game tree using the minimax principle. Practice shows that deeper searches produce better results. However, theoretical analyses indicate that under apparently reasonable conditions, the behavior of minimax is pathological, i.e. deeper searches produce worse results. In this paper, a minimax model that – unlike most work in this area...

In this work we obtain two minimax inequalities in G-convex spaces which extend and improve a large number of generalizations of the Ky Fan minimax inequality and of the von Neumann–Sion minimax principle. © 2005 Elsevier Ltd. All rights reserved.

It is well known that the best equivariant estimator of a variance covari-ance matrix of multivariate normal distribution with respect to the full ane group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a multivari-ate analysis of variance(MANOVA) model and give other classes of minimax estimators.

fθ log (fθ/f̂) is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax. A result resembling Stein’s paradox for estimating normal means by the maximum likelihood holds for the uniform prior in the multivariate location family...

An experimental analysis of some variables of minimax theory.An experimental analysis of some variables of minimax theory.

For simplicity, we focus on the bivariate case (X and Y are each one-dimensional variables). The extension to proof in multivariate case is straight forward. We first work on the mutual information, then show the similar arguments on the copula distances. To prove the theorem, we use Le Cam [1973]’s method to find the lower bound on the minimax risk of the estimating mutual information MI . To ...

Suppose Nature picks a probability measure P on a complete separable metric space X at random from a measurable set P fP g Then without knowing a statistician picks a measure Q on X Finally the statistician su ers a loss D P jjQ the relative entropy between P and Q We show that the minimax and maximin values of this game are always equal and there is always a minimax strategy in the closure of ...

In this paper, we propose a novel implementation of a minimax decision rule for continuous density hidden Markovmodel-based robust speech recognition. By combining the idea of the minimax decision rule with a normal Viterbi search, we derive a recursive minimax search algorithm, where the minimax decision rule is repetitively applied to determine the partial paths during the search procedure. B...

In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful variational analysis...