The paper considers parametric and nonparametric estimation of the distribution function F. Issues of particular interest are the identification properties of this model and, in the nonparametric case, the speed of convergence of the estimator F. The latter depends upon the properties of the...

The problem of approximating a general regression function m(x)= E(Y|X=x) is addressed. As in the case of the classical L2-type projection pursuit regression considered by Hall (1989), we propose to approximate m(x) through a regression of Y given an index, that is a unidimensional projection of X.

In this paper, we estimate the Lyapunov exponent using an adapted nearest neighbord method. We justify our methodology using Monte Carlo methods, on the logistic function and the r-adic map.

Let , be a Markovian, measurable, strictly stationary process taking values in a measurable space (E, ), and g a mapping from E into a separable Hilbert space H. A statistical nonparametric predictor of g([xi]T+h) is studied in the paper. That predictor, based on the observations of the process...

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case...