We introduce a simple new hypothesis testing procedure, which, based on an independent sample drawn from a certain density, detects which of $k$ nominal densities is the true density is closest to, under the total variation (L_{1}) distance. We obtain a density-free uniform exponential bound for...

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combination of several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost...

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary and ergodic random process then the average...