The Empirical Distribution of a Large Number of Correlated Normal Variables.

Motivated by the advent of high dimensional highly correlated data, this work studies the limit behavior of the empirical cumulative distribution function (ecdf) of standard normal random variables under arbitrary correlation. First, we provide a necessary and sufficient condition for convergence of the ecdf to the standard normal distribution. Next, under general correlation, we show that the ecdf limit is a random, possible infinite, mixture of normal distribution functions that depends on a number of latent variables and can serve as an asymptotic approximation to the ecdf in high dimensions.

Matching With Doses in an Observational Study of a Media Campaign Against Drug Abuse.

Multivariate matching with doses of treatment differs from the treatment-control matching in three ways. First, pairs must not only balance covariates, but also must differ markedly in dose. Second, any two subjects may be paired, so that the matching is nonbipartite, and different algorithms are required.