The asymptotic minimax theorem for Bernoully twoarmed bandit problem states that the minimax risk has the order N as N → ∞, where N is the control horizon, and provides lower and upper estimates. It can be easily extended to normal two-armed bandit. For normal two-armed bandit, we generalize the asymptotic minimax theorem as follows: the minimax risk is approximately equal to 0.637N as N →∞. Ke...

The discovery that the minimax decision rule performs poorly in some games has sparked interest in possible alternatives to minimax. Until recently, the only games in which minimax was known to perform poorly were games which were mainly of theoretical interest. However, this paper reports results showing poor performance of minimax in a more common game called kalah. For the kalah games tested...

In this paper we address two important issues about minimax regression designs: existence and symmetry. These designs are robust against possible misspecification of the regression response. Existence is proved for A-optimal, D-optimal and Q-optimal minimax designs. Symmetry is proved for all D-optimal minimax designs and for some special cases of A-optimal and Q-optimal minimax designs.

SUMMARY The minimax kernels for nonparametric function and its derivative estimates are investigated. Our motivation comes from a study of minimax properties of nonparametric kernel estimates of probability densities and their derivatives. The asymptotic expression of the linear maximum risk is established. The corresponding minimax risk depends on the solutions to a kernel variational problem,...

We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear group. These results apply in particular to boundedly generated groups; they imply that every infinite BG residually finite group has an infinite linear quoti...

Suppose the mean responses from m-1 treatment groups in an experiment are to be compared to the mean of a control group. A uniform allocation of observations over the treatment groups is then often used. However, other allocation schemes can give a better precision in the inference. This is particularly emphasised when the variances of the responses are di¤erent in di¤erent treatment groups. He...