We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameter problems. Results rely on the structure of...

Abstract Nonparametric estimation of tail dependence can be based on a standardization of the marginals if their cumulative distribution functions are known. In this paper it is shown to be asymptotically more efficient if the additional knowledge of the marginals is ignored and estimators are...

Abstract We consider a Lévy driven stochastic convolution, also called continuous time Lévy driven moving average model X(t)=\int_{0}^{t}a(t-s)\,dZ(s) , where 𝑍 is a Lévy martingale and the kernel a(\,{.}\,) a deterministic function square integrable on \mathbb{R}^{+} . Given 𝑁 i.i.d....

Summary The Cauchy problem for the one-dimensional heat equation asks for solutions u f ( x,t ) of ∂ u /∂ t = ∂ 2 u / ∂ x 2 on R × [1, ∞) with u ( x , 1) = f ( x ) on R. Here we assume that the initial condition f ( x ), x ∊ R, and hence the solution u f is unknown but that at times...

Summary Microaggregation is a set of procedures that distort empirical data in order to guarantee their factual anonymity. At the same time the information content of data sets should not be reduced too much and should still be useful for scientific research. This paper investigates the effect...

Abstract : In this article, we discuss causal inference when there are multiple versions of treatment. The potential outcomes framework, as articulated by Rubin, makes an assumption of no multiple versions of treatment, and here we discuss an extension of this potential outcomes framework to...