Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density...

We study a generalised version of the logistic map of the unit interval $(0,1)$, in which the point $x$ is taken to $1-|2x-1|^nu$. Here, $nu 0$ is a parameter of the map, which has received attention only when $nu =1$ and 2. We obtain the invariant density when $nu = frac12$, and derive...

Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.

Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling...