Abstract
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]).
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References
Other publications by Ray Carroll cited in this chapter.
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.
Carroll, R. J. (1989). Covariance analysis in generalized linear measurement error models. Statistics in Medicine, 8, 1075–1093.
Carroll, R. J. and Spiegelman, C. H. (1992). Diagnostics for nonlinearity and heteroscedasticity in errors-in-variables regression. Technometrics, 34, 186–196.
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.
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.
Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu, C. M. (2006). Measurement error in nonlinear models, 2nd ed. London: Chapman & Hall.
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.
Carroll, R. J., Delaigle, A., and Hall, P. (2009). Nonparametric Prediction in Measurement Error Models. Journal of the American Statistical Association, 104, 993–1003.
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.
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.
Wei, Y. and Carroll, R. J. (2009). Quantile regression with measurement error. Journal of the American Statistical Association, 104, 1129–1143.
Publications by other authors cited in this chapter.
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.
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.
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.
Byar, D. P. and Gail, M. (1989). Introduction. Errors-in-variables workshop. Statistics in Medicine, 8, 1027–1029.
Cook, J. R. and Stefanski, L. A. (1994). Simulation-extrapolation in parametric measurement error models. Journal of the American Statistical Association, 89, 1314–1328.
Fan, J. and Truong, Y. K. (1993). Nonparametric regression with errors in variables. Annals of Statistics, 21, 1900–1925.
Fuller, W. A. (1987). Measurement error models. New York: John Wiley.
Gleser, L. J. (1990). Improvements of the naive approach to estimation in nonlinear errors-in-variables problems. Contemporary Mathematics, 112, 99–114.
Guolo, A. (2008). A flexible approach to measurement error correction in case-control studies. Biometrics, 64, 1207–1214.
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.
Severini, T. A. and Staniswalis, J. G. (1994). Quasi-likelihood estimation in semiparametric models. Journal of the American Statistical Association, 89, 501–511.
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Buonaccorsi, J.P., Delaigle, A. (2014). Measurement Error. In: Davidian, M., Lin, X., Morris, J., Stefanski, L. (eds) The Work of Raymond J. Carroll. Springer, Cham. https://doi.org/10.1007/978-3-319-05801-6_1
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