We warn of a class of problems that occur when inverting some Characteristic Functions (CFs) which we term confluent. Confluences can arise in joint CFs during the derivation of the marginal density of some lower-dimensional combination of the components. We illustrate with a simple (yet common)...

Kernels are typically justified as a smoothing device in nonparametric analysis. We provide alternative interpretations which could lead to the use of asymmetric kernels. We thus derive the class of optimal asymmetric kernels, and analyse its main properties. We illustrate numerically its...

Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not...

We derive expansions of E(x) in terms of the moments of a transformation of x, in a more general context than Taylor expansions. Apart from the intrinsic interest in such a fundamental relation that links the moments of a variate and its nonlinear transformations, our results can be used in...