Measurement Error

  • John P. Buonaccorsi
  • Aurore Delaigle


It is both a privilege and a challenge to summarize Ray Carroll’s contributions in measurement error. Ray literally wrote the book on the topic with coauthors David Ruppert, Len Stefanski, and Ciprian Crainiceanu (Carroll et al., 2006), and his fingerprints are present in a huge amount of published research on measurement error over the past 30 years. In addition to the book, Ray has authored or coauthored close to 100 papers involving measurement error alone, addressing a vast array of problems. His work covers models from the fairly simple to the very complex with an emphasis ranging from the relatively applied to the highly theoretical. Our detailed discussion of Ray’s work concentrates heavily on the twelve papers appearing in this volume, although this only scratches the surface of his contributions. We first discuss parametric models ([MEM-1]-[MEM-4] and [MEM-7]-[MEM-9]), then turn to non-parametric and semi-parametric models including deconvolution problems ([MEM-5],[MEM-6],[MEM-10]-[MEM-11]).


Measurement Error Statistical Theory Huge Amount Vast Array Deconvolution Problem 
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Other publications by Ray Carroll cited in this chapter.

  1. Carroll, R. J. and Gallo, P. P. (1982). Some aspects of robustness in the functional errors-in-variables regression-model. Communications in Statistics, Part A-Theory and Methods, 11, 2573–2585.CrossRefzbMATHMathSciNetGoogle Scholar
  2. Carroll, R. J. (1989). Covariance analysis in generalized linear measurement error models. Statistics in Medicine, 8, 1075–1093.CrossRefGoogle Scholar
  3. Carroll, R. J. and Spiegelman, C. H. (1992). Diagnostics for nonlinearity and heteroscedasticity in errors-in-variables regression. Technometrics, 34, 186–196.CrossRefMathSciNetGoogle Scholar
  4. Carroll, R. J. and Ruppert, D. (1996). The use and misuse of orthogonal regression in linear errors-in-variables models. American Statistician, 50, 1–6.Google Scholar
  5. Carroll, R. J., Ruppert, D., Crainiceanu, C. M., Tosteson, T. D., and Karagas, M. R. (2004). Nonlinear and nonparametric regression and instrumental variables. Journal of the American Statistical Association, 99, 736–750.CrossRefzbMATHMathSciNetGoogle Scholar
  6. Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu, C. M. (2006). Measurement error in nonlinear models, 2nd ed. London: Chapman & Hall.CrossRefzbMATHGoogle Scholar
  7. Carroll, R. J., Delaigle, A., and Hall, P. (2007). Nonparametric regression estimation from data contaminated by a mixture of Berkson and classical errors. Journal of the Royal Statistical Society, Series B, 69, 859–878.CrossRefMathSciNetGoogle Scholar
  8. Carroll, R. J., Delaigle, A., and Hall, P. (2009). Nonparametric Prediction in Measurement Error Models. Journal of the American Statistical Association, 104, 993–1003.CrossRefMathSciNetGoogle Scholar
  9. Delaigle, A., Fan, J. and Carroll, R.J. (2009). A design-adaptive local polynomial estimator for the errors-in-variables problem. Journal of the American Statistical Association, 104, 348–359.CrossRefMathSciNetGoogle Scholar
  10. Ma, Y. and Carroll, R. J. (2006). Locally efficient estimators for semiparametric models with measurement error. Journal of the American Statistical Association, 101, 1465–1474.CrossRefzbMATHMathSciNetGoogle Scholar
  11. Wei, Y. and Carroll, R. J. (2009). Quantile regression with measurement error. Journal of the American Statistical Association, 104, 1129–1143.CrossRefMathSciNetGoogle Scholar

Publications by other authors cited in this chapter.

  1. Armstrong, B. G., Whittemore, A. S., and Howe, G. R. (1989). Analysis of case-control data with covariate measurement error: Application to diet and colon cancer. Statistics in Medicine, 8, 1151–1163.CrossRefGoogle Scholar
  2. Brown, P. J. and Fuller, W. A. (1990). Statistical Analysis of Measurement Error Models and Applications: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, June 10–16, 1989. Providence: American Mathematical Society.Google Scholar
  3. Buonaccorsi, J. P. (1990). Double sampling for exact values in the normal discriminant model with applications to binary regression. Communications in Statistics, Theory and Methods, 19, 4569–4586.CrossRefzbMATHMathSciNetGoogle Scholar
  4. Byar, D. P. and Gail, M. (1989). Introduction. Errors-in-variables workshop. Statistics in Medicine, 8, 1027–1029.Google Scholar
  5. Cook, J. R. and Stefanski, L. A. (1994). Simulation-extrapolation in parametric measurement error models. Journal of the American Statistical Association, 89, 1314–1328.CrossRefzbMATHGoogle Scholar
  6. Fan, J. and Truong, Y. K. (1993). Nonparametric regression with errors in variables. Annals of Statistics, 21, 1900–1925.CrossRefzbMATHMathSciNetGoogle Scholar
  7. Fuller, W. A. (1987). Measurement error models. New York: John Wiley.CrossRefzbMATHGoogle Scholar
  8. Gleser, L. J. (1990). Improvements of the naive approach to estimation in nonlinear errors-in-variables problems. Contemporary Mathematics, 112, 99–114.CrossRefMathSciNetGoogle Scholar
  9. Guolo, A. (2008). A flexible approach to measurement error correction in case-control studies. Biometrics, 64, 1207–1214.CrossRefzbMATHMathSciNetGoogle Scholar
  10. Rosner, B., Willett, W. C., and Spiegelman, D. (1989). Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine, 8, 1051–1070.CrossRefGoogle Scholar
  11. Severini, T. A. and Staniswalis, J. G. (1994). Quasi-likelihood estimation in semiparametric models. Journal of the American Statistical Association, 89, 501–511.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • John P. Buonaccorsi
    • 1
  • Aurore Delaigle
    • 2
  1. 1.University of MassachusettsAmherstUSA
  2. 2.University of MelbourneMelbourneAustralia

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