Asymptotic expansions for conditional moments of Bernoulli trials

Abstract In this paper we study conditional distributions of independent, but not identically distributed Bernoulli random variables. The conditioning variable is the sum of the Bernoulli variables. We obtain Edgeworth expansions for the conditional expectations and the conditional variances and covariances. The results are of basic interest for several applications, e.g. for the study of conditional maximum likelihood estimation in Rasch models with many item parameters.