Random Calibration With Many Measurements: An Application of Stein Estimation

REFERENCES

• Aitchison , J. and Dunsmore , I. R. 1975 . Statistical Prediction Analysis Cambridge , , U.K. : Cambridge University Press. .
   Google Scholar
• Bock , M. E. , Yancey , T. A. and Judge , G. G. 1973 . “The Statistical Consequences of Preliminary Test Estimators in Regression,” . Journal of the American Statistical Association , 68 : 109 – 116 .
   Web of Science ®Google Scholar
• Brown , P. J. 1982 . “Multivariate Calibration” (with discussion) . Journal of the Royal Statistical Society, Ser. B , 44 : 287 – 321 .
   Google Scholar
• Casella , G. and Hwang , J. T. 1987 . “Employing Vague Prior Information in the Construction of Confidence Sets,” . Journal of Multivariate Analysis , 21 : 70 – 104 .
   Web of Science ®Google Scholar
• Draper , N. R. and Smith , H. 1981 . Applied Regression Analysis, , 2nd Ed. New York : John Wiley. .
   Google Scholar
• Efron , B. and Morris , C. 1973 . “Stein's Estimation Rule and Its Competitors—An Empirical Bayes Approach,” . Journal of the American Statistical Association , 68 : 117 – 130 .
   Web of Science ®Google Scholar
• Efron , B. and Morris , C. 1975 . “Data Analysis Using Stein's Estimator and Its Generalizations,” . Journal of the American Statistical Association , 70 : 311 – 319 .
   Web of Science ®Google Scholar
• Efron , B. and Morris , C. 1976 . “Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution,” . The Annals of Statistics , 4 : 11 – 21 .
   Web of Science ®Google Scholar
• Fearn , T. 1983 . “A Misuse of Ridge Regression in the Calibration of a Near Infrared Reflectance Instrument,” . Applied Statistics , 32 : 73 – 79 .
   Web of Science ®Google Scholar
• Hocking , R. R. 1976 . “The Analysis and Selection of Variables in Linear Regression,” . Biometrics , 32 : 1 – 49 .
   Web of Science ®Google Scholar
• James , W. and Stein , C. “Estimation With Quadratic Loss,” . Proceedings of the Fourth Berkeley Symposium . Vol. 1 , pp. 361 – 379 . Berkeley : University of California Press. .
   Google Scholar
• Jennrich , R. I. and Oman , S. D. 1986 . “How Much Does Stein Estimation Help in Multiple Linear Regression?” . Technometrics , 28 : 113 – 120 .
   Web of Science ®Google Scholar
• Kendall , M. G. 1957 . A Course in Multivariate Analysis London : Charles W. Griffin. .
   Google Scholar
• Lindberg , W. , Persson , J. and Wold , S. 1983 . “Partial Least Squares Method for Spectrofluorimetric Analysis of Mixtures of Humic Acid and Ligninsulfonate,” . Analytical Chemistry , 55 : 643 – 648 .
   Web of Science ®Google Scholar
• Lindley , D. V. 1962 . “Discussion of a Paper by C. Stein,” . Journal of the Royal Statistical Society, Ser B , 24 : 285 – 287 .
   Google Scholar
• Mallows , C. L. 1973 . “Some Comments on Cp“ . Technometrics , 16 : 661 – 675 .
   Google Scholar
• Massy , W. F. 1965 . “Principal Components Regression in Exploratory Statistical Research,” . Journal of the American Statistical Association , 60 : 234 – 256 .
   Web of Science ®Google Scholar
• Naes , T. 1985 . “Multivariate Calibration When the Error Covariance Matrix is Structured,” . Technometrics , 27 : 301 – 311 .
   Web of Science ®Google Scholar
• Naes , T. 1989 . “Leverage and Influence Measures for Principal Component Regression,” . Chemometrics and Intelligent Laboratory Systems , 5 : 155 – 168 .
   Web of Science ®Google Scholar
• Sclove , S. L. 1968 . “Improved Estimators for Coefficients in Linear Regression,” . Journal of the American Statistical Association , 63 : 596 – 606 .
   Web of Science ®Google Scholar
• Scheffé , H. 1959 . The Analysis of Variance New York : John Wiley. .
   Google Scholar
• Sclove , S. L. , Morris , C. and Radhakrishnan , R. 1972 . “Non-optimality of Preliminary Test Estimators for the Multinormal Mean,” . The Annals of Mathematical Statistics , 43 : 1481 – 1490 .
   Google Scholar
• Seber , G. A. F. 1977 . Linear Regression Analysis New York : John Wiley. .
   Google Scholar
• Spjøtvoll , E. , Martens , H. and Volden , R. 1982 . “Restricted Least Squares Estimation of Spectrum and Concentration of Two Unknown Components Available in Mixtures,” . Technometrics , 24 : 173 – 180 .
   Web of Science ®Google Scholar
• Stein , C. 1966 . “An Approach to the Recovery of Inter-block Information in Balanced Incomplete Block Designs”. ” . In Festschrift for J. Neyman: Research Papers in Statistics Edited by: David , F. N. 351 – 366 . New York : John Wiley. .
   Google Scholar
• Stein , C. 1981 . “Estimation of the Mean of a Multivariate Normal Distribution,” . The Annals of Statistics , 9 : 1135 – 1151 .
   Web of Science ®Google Scholar
• Yancey , T. A. and Judge , G. G. 1976 . “A Monte Carlo Comparison of Traditional and Stein-Rule Estimators Under Squared Error Loss,” . Journal of Econometrics , 4 : 285 – 294 .
   Google Scholar