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February 2005 Combining information from independent sources through confidence distributions
Kesar Singh, Minge Xie, William E. Strawderman
Ann. Statist. 33(1): 159-183 (February 2005). DOI: 10.1214/009053604000001084

Abstract

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.

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Kesar Singh. Minge Xie. William E. Strawderman. "Combining information from independent sources through confidence distributions." Ann. Statist. 33 (1) 159 - 183, February 2005. https://doi.org/10.1214/009053604000001084

Information

Published: February 2005
First available in Project Euclid: 8 April 2005

zbMATH: 1064.62003
MathSciNet: MR2157800
Digital Object Identifier: 10.1214/009053604000001084

Subjects:
Primary: 62F03 , 62F12 , 62G05 , 62G10 , 62G20

Keywords: bootstrap , combining information , common mean problem , computer intensive methods , confidence distribution , frequentist inference , Meta-analysis , p-value function , robust scale , U-statistic

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • February 2005
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