Considering homosexual contacts and heterosexual contacts in the course of sexual contacts, double degrees which describe the numbers of homosexual contacts and heterosexual contacts are introduced, correlation coefficients about degrees based on the joint probability distribution are given, and...

Summary We consider sequences of random variables with distributions that satisfy recurrences as they appear for quantities on random trees, random combinatorial structures and recursive algorithms. We study the tails of such random variables in cases where after normalization convergence to the...

We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. Normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the...

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator...

We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends only on the set itself and on the covariance matrix of...