Asymptotic Results for a Generalized Pólya Urn with “Multi-Updating” and Applications to Clinical Trials

Abstract

In this article, a new Pólya urn model is introduced and studied; in particular, a strong law of large numbers and two central limit theorems are proved. This urn generalizes a model studied in Berti et al. (2004), May et al. (2005), and in Crimaldi (2007), and it has natural applications in clinical trials. Indeed, the model includes both delayed and missing (or null) responses. Moreover, a connection with the conditional identity in distribution of Berti et al. (2004) is given.