Nonparametric prediction in measurement error models

Journal of the American Statistical Association

Volumn 104, Issue 487, 2009, Pages 993-1003

  Carroll, Raymond J ^a   Delaigle, Aurore ^b,c   Hall, Peter ^c,d  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c UNIVERSITY OF MELBOURNE   (Australia)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bandwidth; Contamination; Deconvolution; Errors in variables; Parametric rates; Regression; Ridge parameter; Smoothing

Indexed keywords

EID: 70349772326     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2009.tm07543     Document Type: Article

References (56)

1. Berry, S., Carroll, R. J., and Ruppert, D. (2002), "Bayesian Smoothing and Regression Splines for Measurement Error Problems, " Journal of the American Statistical Association, 97, 160-169.
2. Carroll, R. J., and Hall, P. (1988), "Optimal Rates of Convergence for Deconvolving a Density, " Journal of the American Statistical Association, 83, 1184-1186.
3. Carroll, R. J., Maca, J. D., and Ruppert, D. (1999), "Nonparametric Regression in the Presence of Measurement Error, " Biometrika, 86, 541-554.
4. Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.), Boca Raton: Chapman & Hall/CRC Press.
5. Cheng, C.-L., and Riu, J. (2006), "On Estimating Linear Relationships When Both Variables Are Subject to Heteroscedastic Measurement Errors, " Technometrics, 48, 511-519.
6. Cook, J. R., and Stefanski, L. A. (1994), "Simulation-Extrapolation Estimation in Parametric Measurement Error Models, " Journal of the American Statistical Association, 89, 1314-1328.
7. Delaigle, A. (2007), "Nonparametric Density Estimation From Data With a Mixture of Berkson and Classical Errors, " The Canadian Journal of Statistics, 35, 89-104.
8. Delaigle, A., and Meister, A. (2007), "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem, " Journal of the American Statistical Association, 102, 1416-1426.
9. (2008), "Density Estimation With Heteroscedastic Error, " Bernoulli, 14, 562-579.
10. 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.
11. Delaigle, A., Hall, P., and Meister, A. (2008), "On Deconvolution With Repeated Measurements, " The Annals of Statistics, 36, 665-685.
12. Devanarayan, V., and Stefanski, L. A. (2002), "Empirical Simulation Extrapolation for Measurement Error Models With Replicate Measurements, " Statistics & Probability Letters, 59, 219-225.
13. Fan, J. (1991), "On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems, " The Annals of Statistics, 19, 1257-1272.
14. Fan, J., and Truong, Y. K. (1993), "Nonparametric Regression With Errors in Variables, " The Annals of Statistics, 21, 1900-1925.
15. Ferrari, P., Day, N. E., Boshuizen, H. C., Roddam, A., Hoffmann, K., Thiebaut, A., Pera, G., Overvad, K., Lund, E., Trichopoulou, A., Tumino, R., Gullberg, A., Norat, T., Slimani, N., Kaaks, R., and Riboli, E. (2008), "The Evaluation of the Diet/Disease Relation in the EPIC Study: Considerations for the Calibration and the Disease Models, " International Journal of Epidemiology, 37, 368-378.
16. Ferrari, P., Kaaks, R., Fahey, M. T., Slimani, N., Day, N. E., Pera, G., Boshuizen, H. C., Roddam, A., Boeing, H., Nagel, G., Thiebaut, A., Orfanos, P., Krogh, P., Braaten, T., and Riboli, E. (2004), "Within- and Between-Cohort Variation in Measured Macronutrient Intakes, Taking Account of Measurement Errors, in the European Prospective Investigation Into Cancer and Nutrition Study, " American Journal of Epidemiology, 160, 814-822.
17. Flagg, E. W., Coates, R. J., Calle, E. E., Potischman, N., and Thun, M. (2000), "Validation of the American Cancer Society Cancer Prevention Study II Nutrition Survey Cohort Food Frequency Questionnaire, " Epidemiology, 11, 462-468.
18. Hall, P., and Meister, A. (2007), "A Ridge-Parameter Approach to Deconvolution, " The Annals of Statistics, 35, 1535-1558.
19. Hu, Y., and Schennach, S. M. (2008), "Identification and Estimation of Nonclassical Nonlinear Errors-in-Variables Models With Continuous Distributions, " Econometrica, 76, 195-216.
20. Huang, X. Z., Stefanski, L. A., and Davidian, M. (2006), "Latent-Model Robustness in Structural Measurement Error Models, " Biometrika, 93, 53-64.
21. Kim, J., and Gleser, L. J. (2000), "SIMEX Approaches to Measurement Error in ROC Studies, " Communications in Statistics. Theory and Methods, 29, 2473-2491.
22. Kulathinal, S. B., Kuulasmaa, K., and Gasbarra, D. (2002), "Estimation of an Errors-in-Variables Regression Model When the Variances of the Measurement Errors Vary Between the Observations, " Statistics in Medicine, 21, 1089-1101.
23. Li, T., and Vuong, Q. (1998), "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators, " Journal of Multivariate Analysis, 65, 139-165.
24. Linton, O., and Whang, Y. J. (2002), "Nonparametric Estimation With Aggregated Data, " Econometric Theory, 18, 420-468.
25. Marron, J. S., andWand, M. P. (1992), "Exact Mean Integrated Squared Error, " The Annals of Statistics, 20, 712-736.
26. National Research Council, Committee on Pesticides in the Diets of Infants and Children (1993), Pesticides in the Diets of Infants and Children, Washington, DC: National Academies Press.
27. Schennach, S. M. (2004a), "Estimation of Nonlinear Models With Measurement Error, " Econometrica, 72, 33-75.
28. (2004b), "Nonparametric Regression in the Presence of Measurement Error, " Econometric Theory, 20, 1046-1093.
29. Simonoff, J. S. (1996), Smoothing Methods in Statistics, New York: Springer.
30. Staudenmayer, J., and Ruppert, D. (2004), "Local Polynomial Regression and Simulation-Extrapolation, " Journal of the Royal Statistical Society, Ser. B, 66, 17-30.
31. Staudenmayer, J., Ruppert, D., and Buonaccorsi, J. (2008), "Density Estimation in the Presence of Heteroskedastic Measurement Error, " Journal of the American Statistical Association, 103, 726-736.
32. Stefanski, L. A. (2000), "Measurement ErrorModels, " Journal of the American Statistical Association, 95, 1353-1358.
33. Stefanski, L. A., and Carroll, R. J. (1990), "Deconvoluting Kernel Density Estimators, " Statistics, 21, 165-184.
34. Taupin, M. L. (2001), "Semi-Parametric Estimation in the Nonlinear Structural Errors-in-Variables Model, " The Annals of Statistics, 29, 66-93.
35. Thamerus, M. (2003), "Fitting a Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Errors, " Computational Statistics, 18, 1-17.
36. Wand, M. P., and Jones, M. C. (1995), Kernel Smoothing, London: Chapman & Hall.
37. Andrews, D. W. K. (1995), "Nonparametric Kernel Estimation for Semiparametric Models, " Econometric Theory, 11, 560-596.
38. Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), Measurement Error in Nonlinear Models, New York: Chapman & Hall.
39. Hsiao, C. (1989), "Consistent Estimation for Some Nonlinear Errors-in- Variables Models, " Journal of Econometrics, 41, 159-185.
40. Li, T. (2002), "Robust and Consistent Estimation of Nonlinear Errors-in- Variables Models, " Journal of Econometrics, 110, 1-26.
41. McIntyre, J., and Stefanski, L. A. (2009), "Heteroscedastic Measurement Deconvolution, " Annals of the Institute of Statistical Mathematics, to appear.
42. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge, U.K.: Cambridge University Press.
43. Bissantz, N., D̈mbgen, L., Holzmann, H., and Munk, A. (2007), "Nonparametric Confidence Bands in Deconvolution Density Estimation, " Journal of the Royal Statistical Society, Ser. B, 69, 483-506.
44. Sun, J. (1993), "Tail Probabilities of the Maxima of Gaussian Random Fields, " The Annals of Probability, 21, 34-71.
45. Sun, J., Morrison, H., Harding, P., and Woodroofe, M. (2002), "Density and Mixture Estimation From Data With Measurement Errors, " manuscript, available at http://sun.cwru.edu/~jiayang/india.ps.
46. Sun, J., Wang, X., and Woodroofe, M. (2009), "Non-Fourier Deconvolution Density Estimation in Measurement Error Problems, " manuscript.
47. Wang, X., and Sun, J. (2009), "New Procedures for Nonparametric Regression With Errors in Variables, " manuscript.
48. Wang, X., Sun, J., and Fan, Z. (2009), "Deconvolution Density EstimationWith Heteroscedastic Error Using SIMEX, " manuscript.
49. Carroll, R. J., and Stefanski, L. A. (1990), "Approximate Quasilikelihood Estimation in Models With Surrogate Predictors, " Journal of the American Statistical Association, 85, 652-663.
50. Duncan, G. T., andMukherjee, S. (2000), "Optimal Disclosure Limitation Strategy in Statistical Databases: Deterring Tracker Attacks Through Additive Noise, " Journal of the American Statistical Association, 95, 720-729.
51. Duncan, G. T., and Pearson, R. W. (1991), "Enhancing Access to Data While Protecting Confidentiality: Prospects for the Future, " Statistical Science, 3, 219-239.
52. Fuller, W. A. (1993), "Masking Procedures for Microdata Disclosure Limitation, " Journal of Official Statistics, 9, 383-406.
53. Gomatam, S., Karr, A. F., Reiter, J. P., and Sanil, A. P. (2005), "Data Dissemination and Disclosure Limitation in aWorldWithout Microdata: A Riskutility Framework for Remote Access Analysis Servers, " SS, 20 (2), 163-177.
54. Sullivan, G., and Fuller, W. A. (1989), "The Use of Measurement Error to Avoid Disclosure, " in Proceedings of the Survey Research Methods Section, Alexandria, VA: American Statistical Association, pp. 802-807.
55. Tendick, P. (1991), "Optimal Noise Addition for Preserving Confidentiality in Multivariate Data, " Journal of Statistical Planning & Inference, 27, 341- 353.
56. (1992), "Assessing the Effectiveness of the Noise Addition Method of Preserving Confidentiality in the Multivariate Normal Case, " Journal of Statistical Planning & Inference, 31, 273-282.