2005/02/01 by Kesar Singh, Minge Xie, William E. Strawderman
Mathematics · #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #math.ST #msc:62F03 #msc:62F12 #msc:62G05 #msc:62G10 #msc:62G20. #stat.TH
paper · pdf · doi:10.1214/009053604000001084
published as Annals of Statistics 2005, Vol. 33, No. 1, 159-183 · Published at http://dx.doi.org/10.1214/009053604000001084 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/02/01 · arxiv created 2005/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops new methodology, together with related theories, for combining information from independent studies through confidence distributions. A formal definition of a confidence distribution and its asymptotic counterpart (i.e., asymptotic confidence distribution) are given and illustrated in the context of combining information. Two general combination methods are developed: the first along the lines of combining p-values, with some notable differences in regard to optimality of Bahadur type efficiency; the second by multiplying and normalizing confidence densities. The latter approach is inspired by the common approach of multiplying likelihood functions for combining parametric information. The paper also develops adaptive combining methods, with supporting asymptotic theory which should be of practical interest. The key point of the adaptive development is that the methods attempt to combine only the correct information, downweighting or excluding studies containing little or wrong information about the true parameter of interest. The combination methodologies are illustrated in simulated and real data examples with a variety of applications.