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There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitati
We investigate the tail behaviour of the steady state distribution of a stochastic recursion that generalises Lindleys recursion. This recursion arises in queuing systems with dependent interarrival and service times, and includes alternating service
An urn contains black and red balls. Let $Z_n$ be the proportion of black balls at time $n$ and $0leq L<Uleq 1$ random barriers. At each time $n$, a ball $b_n$ is drawn. If $b_n$ is black and $Z_{n-1}<U$, then $b_n$ is replaced together with a random
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density estimator
The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper we propose a concept of local association, where highly connected components in a graphical
Though Gaussian graphical models have been widely used in many scientific fields, limited progress has been made to link graph structures to external covariates because of substantial challenges in theory and computation. We propose a Gaussian graphi