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Predictive Distributions in the Presence of Measurement Errors

Published online by Cambridge University Press:  27 July 2009

Irwin Guttman  and
Ulrich Menzefricke
Irwin Guttman
Affiliation:
Department of Statistics, Suny at Buffalo, 249 Farber Hall, 3435 Main Street, Buffalo, New York 14214
Ulrich Menzefricke
Affiliation:
Faculty of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada, M5S 3E6
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Extract

We consider a hierarchical linear regression model where the regression parameters for the units have a multivariate normal distribution whose parameters are unknown. Several replications are available for each unit. The design matrices for the units need not be the same. A complicating feature of the model is that each observation is subject to measurement error. The objective of the paper is to derive the predictive distribution of the “true” value of the response at a given design point. A Bayesian treatment is given to the problem. In addition to standard prior distributions, other prior distributions are considered. The calculations are done with the Gibbs sampler. An example is discussed in detail.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 601 - 611
Copyright
Copyright © Cambridge University Press 1996

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References

1.DuMouchel, W. & Waternaux, C. (1992). Hierarchical models for combining information and for meta-analyses (discussion). In Bernardo, J., Berger, J., Dawid, A., & Smith, A.F.M. (eds.), Bayesian statistics, Vol. 4. Oxford: Clarendon Press, pp. 338–341.Google Scholar
2.Gelfand, A.E. & Smith, A.F.M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association 85: 398–409.Google Scholar
3.Odell, P.L. & Feiveson, A.H. (1966). A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association 61: 199–203.Google Scholar
4.Ritter, C. & Tanner, M.A. (1992). The Gibbs stopper and the griddy Gibbs sampler. Journal of the American Statistical Association 87: 861–868.Google Scholar
5.Wang, C.M. & Iyer, H.K. (1995). Tolerance intervals for the distribution of true values in the presence of measurement errors. Technometrics 36: 162–170.CrossRefGoogle Scholar