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Statistica Sinica 20 (2010), 787-805



Andrew L. Rukhin

National Institute of Standards and Technology
and University of Maryland at Baltimore County

Abstract: A method is suggested for constructing a conservative confidence region for the parameters of a linear model on the basis of a linear estimator. In meta-analytical applications, when the results of independent but heterogeneous studies are to be combined, this region can be employed with little to no knowledge of error variances. The formulas for the smallest volume and the corresponding critical constant are derived. The method is compared to several resampling schemes by Monte Carlo simulation, and particular cases of one or two parameters are examined.

Key words and phrases: Dirichlet averages, general linear model, jackknife variance estimators, meta-analysis, quadratic forms in normal vectors, weighted bootstrap.

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