Bootstrapping in controlled calibration experiments

Technometrics

Volumn 41, Issue 3, 1999, Pages 224-233

  Jones, Geoffrey ^a   Rocke, David M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Confidence intervals; ELBA; Immunoassay; Inverse estimation; Nonlinear multivariate regression; Replication

Indexed keywords

ASSAYS; CALIBRATION; COMPOSITION; COMPUTER SIMULATION; DATA STRUCTURES; INVERSE PROBLEMS; NONLINEAR EQUATIONS; PARAMETER ESTIMATION; REGRESSION ANALYSIS;

BOOTSTRAPPING; CONCENTRATIONS; CONFIDENCE INTERVALS; DATASETS; IMMUNOASSAY; INVERSE ESTIMATION; NONLINEAR MULTIVARIATE REGRESSION; REPLICATION;

STATISTICAL METHODS;

EID: 0032683785     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1999.10485671     Document Type: Article

References (35)

1. Bonate, P. L. (1993), “Approximate Confidence Intervals in Calibration Using the Bootstrap,” Analytical Chemistry, 65, 1367-1372.
2. Brown, P. J. (1982), “Multivariate Calibration,” Journal of the Royal Statistical Society, Ser. B, 44, 287-321.
3. Brown, P. J., and Sundberg, R. (1987), “Confidence and Conflict in Multivariate Calibration,” Journal of the Royal Statistical Society, Ser. B, 49, 46-57.
4. Carroll, R. J., and Ruppert, D. (1991), “Prediction and Tolerance Intervals With Transformation and/or Weighting,” Technometrics, 33, 197-210.
5. Clarke, G. P. Y. (1992), “Inverse Estimates From a Multiresponse Model,” Biometrics, 48, 1081-1094.
6. Efron, B. (1979), “Bootstrap Methods: Another Look at the Jackknife,” The Annals of Statistics, 1, 1-26.
7. Efron, B., and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, New York: Chapman and Hall.
8. Fieller, E. C. (1954), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society, Ser. B, 16, 175-185.
9. Freedman, D. A. (1981), “Bootstrapping Regression Models,” The Annals of Statistics, 9, 1218-1228.
10. Gruet, M.-A., and Jolivet, E. (1993), “Calibration With a Nonlinear Standard Curve: How to Do It?” Computational Statistics, 9, 249-276.
11. Hall, P. (1992), The Bootstrap and Edgeworth Expansion, New York: Springer-Verlag.
12. Hardle, W., and Mammen, E. (1991), “Bootstrap Methods for Nonpara-metric Regression,” in Nonparametric Functional Estimation and Related Topics (Series C: Mathematical and Physical Sciences, Vol. 335), ed. G. Roussas, Amsterdam: Kluwer, pp. 111-124.
13. Jones, G. (1996), “The Statistics of Multiple Immunoassay,” unpublished Ph.D. thesis, University of California at Davis, Division of Statistics.
14. Jones, G., Wortberg, M., Kreissig, S. B., Bunch, D. S., Gee, S. J., Hammock, B. D., and Rocke, D. M. (1994), “Extension of the Four-Parameter Logistic Model for ELISA to Multianalyte Analysis,” Journal of Immunology Methods, 177, 1-7.
15. Jones, G., Wortberg, M., Kreissig, S. B., Gee, S. J., Hammock, B. D., and Rocke, D. M. (1995), “Sources of Experimental Variation in Calibration Curves for Enzyme-Linked Immunosorbent Assay,” Analytica Chimica Acta, 313, 197-207.
16. Jones, G., Wortberg, M., Kreissig, S. B., Hammock, B. D., and Rocke, D. M. (1996), “On the Application of the Bootstrap to Calibration Experiments,” Analytical Chemistry, 68, 763-770.
17. Knafl, G., Spiegelman, C., Sacks, J., and Ylvisaker, D. (1984), “Nonparametric Calibration,” Technometrics, 26, 233-241.
18. Krutchkoff, R. G. (1967), “Classical and Inverse Regression Methods of Calibration,” Technometrics, 9, 425-439.
19. Mammen, E. (1992), When Does Bootstrap Work? Asymptotic Results and Simulations, New York: Springer-Verlag.
20. Mathew, T., and Kasala, S. (1994), “An Exact Confidence Region in Multivariate Calibration,” The Annals of Statistics, 22, 94-105.
21. Mathew, T., and Zha, W. (1996), “Conservative Confidence Regions in Multivariate Calibration,” The Annals of Statistics, 24, 707-725.
22. Mee, R. W., Eberhardt, K. R., and Reeve, C. P. (1991), “Calibration and Simultaneous Tolerance Intervals for Regression,” Technometrics, 33, 211-219.
23. O’Connell, M. A., Belanger, B. A., and Haaland, P. D. (1992), “Calibration and Assay Development Using the Four-Parameter Logistic Model,” Chemometrics and Intelligent Laboratory Systems, 20, 97-114.
24. Oman, S. D. (1988), “Confidence Regions in Multivariate Calibration,” The Annals of Statistics, 16, 174-187.
25. Racine-Poon, A., Weihs, C., and Smith, A. F. M. (1991), “Estimation of Relative Potency With Sequential Dilution Errors in Radioimmunoassay,” Biometrics, 47, 1235-1246.
26. Rocke, D. M., and Jones, G. (1997), “Optimal Design for ELISA and other Forms of Immunoassay,” Technometrics, 39, 162-170.
27. Rodbard, D. (1981), “Mathematics and Statistics of Ligand Assays: An Illustrated Guide,” in Ligand Assay: Analysis of International Developments on Isotopin and Nonisotopic Immunoassay, eds. J. Langan and J. J. Clapp, New York: Masson.
28. Rosen, O., and Cohen, A. (1995), “Constructing a Bootstrap Confidence Interval for the Unknown Concentration in Radioimmunoassay,” Statistics in Medicine, 14, 935-952.
29. Scheffe, H. (1973), “A Statistical Theory of Calibration,” The Annals of Statistics, 1, 1-37.
30. Schwenke, J. R., and Milliken, G. A. (1991), “On the Calibration Problem Extended to Nonlinear Models,” Biometrics, 47, 563-574.
31. Scott, D. W. (1992), Multivariate Density Estimation, New York: Wiley.
32. Seber, G. A. F., and Wild, C. J. (1989), Nonlinear Regression, New York: Wiley.
33. Stuart, A., and Ord, J. K. (1987), Kendall’s Advanced Theory of Statistics (5th ed.), Oxford, U.K.: Oxford University Press.
34. Wortberg, M., Jones, G., Kreissig, S. B., Rocke, D. M., and Hammock, B. D. (1995), “An Immunoarray for the Simultaneous Determination of Multiple Triazine Herbicides,” Analytica Chimica Acta, 304, 339-352.
35. Zeng, Q., and Davidian, M. (1997), “Bootstrap Adjusted Calibration Confidence Intervals for Immunoassay,” Journal of the American Statistical Association, 92, 278-290.