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Reducing data nonconformity in linear models

Andrew L. Rukhin

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Procedures to reduce nonconformity in interlaboratory studies by shrinking multivariate data toward a consensus matrix-weighted mean are discussed. Some of them are shown to have a smaller quadratic risk than the ordinary least squares rule. Bayes procedures and shrinkage estimators in random effects models are also considered. The results are illustrated by an example of collaborative studies.

Chapter information

Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 64-77

First available in Project Euclid: 14 March 2012

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Zentralblatt MATH identifier

Primary: 62C20: Minimax procedures
Secondary: 62F10: Point estimation 62P30: Applications in engineering and industry

Birge ratio consensus value jackknife estimator matrix weighted means meta-analysis normal mean shrinkage estimator

Copyright © 2012, Institute of Mathematical Statistics


Rukhin, Andrew L. Reducing data nonconformity in linear models. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 64--77, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL805.

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  • Beckenbach, E. F. and Bellman, R. (1961). Inequalities, Springer, Berlin.
  • DerSimonian, R. and Laird, N. (1986). Meta-analysis in clinical trials. Control. Clin. Trials, 7, 177–188.
  • Fourdrinier, D., Strawderman, W. E. and Wells, M. T. (2003). Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix. J. Mult. Anal. 85, 24–39.
  • Gruber, M. H. J. (1998). Improving Efficiency by Shrinkage: the James-Stein and Ridge Regression Estimators, M. Dekker, New York.
  • Hartung, J., Knapp, G. and Sinha, B. K. (2008). Statistical Meta-Analysis with Applications, Wiley, New York.
  • Hedges, L. V. and Olkin I. (1985). Statistical Methods for Meta-Analysis, Academic Press, London.
  • Lee, Y. and Birkes, D. (1994). Shrinking toward submodels in regression. J. Statist. Plann. Inf. 41, 95–111.
  • Lehmann, E. and Casella, G. (1998). Theory of Point Estimation, 2nd ed., Springer, New York.
  • Paule, R. C. and Mandel, J. (1971). Analysis of interlaboratory measurements on the vapor pressure of cadmium and silver. National Bureau of Standards Special Publication, 260-21, Washington DC.
  • Rukhin, A. L. (1987). How much better are better estimators of a normal variance. J. Amer. Statist. Assoc. 82, 925–928.
  • Rukhin, A. L. (2007). Estimating common vector mean in interlaboratory studies. J. Mult. Anal. 98, 435–434.
  • Rukhin, A. L. (2011). Estimating common parameters in heterogeneous mixed effects model, J. Statist. Plann. Inf. 141, 3181–3192.
  • Strawderman, W. E. and Rukhin, A. L. (2010). Simultaneous estimation and reduction of data nonconformity in interlaboratory studies. J. Royal Statist. Soc., Ser B. 72, 219–234.
  • Wu, C. J. F. (1986). Jackknife, bootstrap and other resampling methods in regression analysis, (with discussion). Ann. Statist. 41, 1261–1350.