ASYMPTOTICS IN RANDOMIZED URN MODELS

Abstract

Advances in Statistics, pp. 334-360 (2008) No AccessASYMPTOTICS IN RANDOMIZED URN MODELSZHI-DONG BAI and FEIFANG HUZHI-DONG BAICollege of Mathematics and Statistics, Northeast Normal University, Changchun, ChinaDepartment of Statistics and Applied Probability, National University of Singapore, SingaporeSupported by NSFC Grant 201471000 and NUS Grant R-155-000-030-112. and FEIFANG HUDepartment of Statistics, Halsey Hall, University of Virginia, Charlottesville, Virginia 22904-4135, USASupported by NSF Grant DMS-0204232 and NUS Grant R-155-000-030-112.https://doi.org/10.1142/9789812793096_0019Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1, 2, …, n - 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition and the patient allocation under general assumptions on random generating matrices which determine how balls are added to the urn. Also we obtain explicit forms of the asymptotic variance-covariance matrices of both the urn composition and the patient allocation. The conditions on the nonhomogeneity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed. Keywords: Asymptotic normalityextended Pólya's urn modelsgeneralized Friedman's urn modelmartingalenonhomogeneous generating matrixresponse-adaptive designsstrong consistencyAMSC: Primary 62E20, Primary 62L05, secondary 62F12 FiguresReferencesRelatedDetails Recommended Advances in Statistics Metrics History KeywordsAsymptotic normalityextended Pólya's urn modelsgeneralized Friedman's urn modelmartingalenonhomogeneous generating matrixresponse-adaptive designsstrong consistencyPDF download

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