Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity

Extremes - Reciprocity characterizes the information exchange between users in a network, and some empirical studies have revealed that social networks have a high proportion of reciprocal edges....     

Hidden Regular Variation, Second Order Regular Variation and Asymptotic Independence

We survey the related asymptotic properties of multivariate distributions; (i) asymptotic independence, (ii) hidden regular variation, and (iii) multivariate second order regular variation. Connections and implications are discussed. The point of view of convergence of measures is emphasized in formulations because we are interested in the concepts being coordinate system free, whenever possible.     

Modeling multiple risks: hidden domain of attraction

A sub-model of multivariate regular variation called hidden regular variation facilitates more accurate estimation of joint tail probabilities in the presence of asymptotic independence. A related concept called hidden domain of attraction can sometimes offer similar estimation assistance in circumstances where hidden regular variation is absent. Examples and discussion illustrate strengths and limitations of this concept. We outline estimation techniques where applicable.     

On the observation closest to the origin

Out of n i.i.d. random vectors in $\text{R}$^d let X¹_n be the one closest to the origin. We show that X¹_n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation. The result is then applied to a problem of density estimation.