Covariances in Pólya urn schemes. Issue 1 (January 2023)

• Record Type: Journal Article
• Authors: Mahmoud, Hosam
• Is Part Of: Probability in the engineering and informational sciences. Volume 37:Issue 1(2023)
• Page Start: 60
• Page End: 71
• Publication Date: 2023-01
• Subjects: L2-limit theorems -- Pólya urn; 60C05 -- 60F25 -- 60K40; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964821000450
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract: By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are "structural, " our purpose here is "computational." We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.