Summary A nonparametric probability density estimation problem is studied for the Bahadur-type risk under the sup-norm losses. The risk is minimax over the Hölder classes of densities. The large sample limiting performance of this risk is found, and the links to asymptotic equivalent...

A binary image model is studied with a Lipschitz edge function. The indicator function of the image is observed in random noise at n design points that can be chosen sequentially. The asymptotically minimax rate as n--[infinity] is found in estimating the edge function, and an asymptotically...

Let G be that portion of the unit square which lies below the graph of a smooth function. Assume that observations of the indicator function of G are available at any points X1,...,Xn in the plane. If each consecutive point Xi can be chosen sequentially, on the basis of all the preceding data,...