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...

Abstract In recent years optimal portfolio selection strategies for sequential investment have been shown to exist. Although their asymptotical optimality is well established, finite sample properties do need the adjustment of parameters that depend on dimensionality and scale. In this paper we...

Summary Regression analysis of a response variable Y requires careful selection of explanatory variables. The quality of a set of explanatory features X =( X (1) ,..., X ( d ) ) can be measured in terms of the minimum mean squared error . This paper investigates methods for estimating L * from...

Abstract 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...