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...

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 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...

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

We consider f-disparities between discrete distributions pn=(pn1,...,pnkn) and their estimates based on relative frequencies in an i.i.d. sample of size n, where is twice continuously differentiable in a neighborhood of 1 with f''(1)[not equal to]0. We derive asymptotic distributions of the...

The purpose of this paper is to introduce an approximation of the kernel-based log-optimal investment strategy that guarantees an almost optimal rate of growth of the capital under minimal assumptions on the behavior of the market. The new strategy uses much less knowledge on the distribution of...

Consider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x)=E{Y|X=x}, this paper investigates methods for estimating the density of the residual Y−m(X) from independent and identically distributed data. For...