The Annals of Statistics

Combining information from independent sources through confidence distributions

Kesar Singh, Minge Xie, and William E. Strawderman

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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.

Article information

Ann. Statist. Volume 33, Number 1 (2005), 159-183.

First available in Project Euclid: 8 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62F12: Asymptotic properties of estimators 62G05: Estimation 62G10: Hypothesis testing 62G20: Asymptotic properties

Combining information confidence distribution frequentist inference bootstrap common mean problem meta-analysis U-statistic robust scale computer intensive methods p-value function


Singh, Kesar; Xie, Minge; Strawderman, William E. Combining information from independent sources through confidence distributions. Ann. Statist. 33 (2005), no. 1, 159--183. doi:10.1214/009053604000001084.

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