Given a dictionary of Mn initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of aggregation for these lq-aggregation problems, our multi-directional (or adaptive...

Based on two independent samples X1, ...,Xm and Xm+1, ...,Xn drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q. The construction is built from randomized nearest-neighbor statistics. It does not require any preliminary information abou...

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,...