Teaching about Approximate Confidence Regions Based on Maximum Likelihood Estimation

References

• Agresti , A. 1990 . Categorical Data Analysis , New York : John Wiley .
   Google Scholar
• Anscombe , F. J. 1964 . “Normal Likelihood Functions” . Annals of the Institute of Statistical Mathematics , 16 : 1 – 19 .
   Web of Science ®Google Scholar
• Arnold , B. C. , Beaver , R. J. , Groeneveld , R. A. and Meeker , W. Q. 1993 . “The Nontruncated Marginal of a Truncated Bivariate Normal Distribution” . Psychometrika , 58 : 471 – 488 .
   Web of Science ®Google Scholar
• Bain , L. J. and Engelhardt , M. 1987 . Introduction to Probability and Mathematical Statistics , Boston : PWS Publishers .
   Google Scholar
• Bates , D. M. and Watts , D. G. 1988 . Nonlinear Regression Analysis and Its Applications , New York : John Wiley .
   Google Scholar
• Beale , E. M. L. 1960 . “Confidence Regions in Nonlinear Regression” . Journal of the Royal Statistical Society , 22 : 41 – 88 . (with discussion), Ser. B
   Google Scholar
• Box , G. E. P. and Jenkins , G. W. 1976 . Time Series Analysis: Forecasting and Control, , revised ed. , San Francisco : Holden-Day .
   Google Scholar
• Casella , G. and Berger , R. L. 1990 . Statistical Inference , Belmont , CA : Wadsworth .
   Google Scholar
• Chernoff , H. 1954 . “On the Distribution of the Likelihood Ratio” . Annals of Mathematical Statistics , 25 : 573 – 578 .
   Google Scholar
• Cook , R. D. and Weisberg , S. 1990 . “Confidence Curves in Nonlinear Regression” . Journal of the American Statistical Association , 85 : 544 – 551 .
   Web of Science ®Google Scholar
• Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• Cox , D. R. and Oakes , D. 1984 . Analysis of Survival Data , New York : Methuen .
   Google Scholar
• Cressie , N. A. C. 1991 . Spatial Statistics , New York : John Wiley .
   Google Scholar
• Donaldson , J. R. and Schnabel , R. B. 1987 . “Computational Experience with Confidence Regions and Confidence Intervals for Nonlinear Least Squares” . Technometrics , 29 : 67 – 82 .
   Web of Science ®Google Scholar
• Feder , P. I. 1968 . “On the Distribution of the Log Likelihood Ratio Statistic When the True Parameter is Close to the Boundary of the Hypothesis Regions” . Annals of Mathematical Statistics , 39 : 2044 – 2055 .
   Google Scholar
• Fuller , W. A. 1987 . Measurement Error Models , New York : John Wiley .
   Google Scholar
• Hahn , G. J. and Meeker , W. Q. 1991 . Statistical Intervals: A Guide for Practitioners , New York : John Wiley .
   Google Scholar
• Kalbfleisch , J. D. and Prentice , R. L. 1980 . The Statistical Analysis of Failure Time Data , New York : John Wiley .
   Google Scholar
• Kalbfleisch , J. D. and Sprott , D. A. 1970 . “Applications of Likelihood Methods to Models Involving Large Numbers of Parameters” . Journal of the Royal Statistical Society , 32 : 175 – 208 . (with discussion), Ser. B
   Google Scholar
• Lawless , J. F. 1982 . Statistical Models and Methods for Life Time Data , New York : John Wiley .
   Google Scholar
• Lehmann , E. L. 1983 . Theory of Point Estimation , New York : John Wiley .
   Google Scholar
• Lehmann , E. L. 1986 . Testing Statistical Hypotheses, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Meeker , W. Q. 1987 . “Limited Failure Population Life Tests: Application to Integrated Circuit Reliability” . Technometrics , 29 : 51 – 65 .
   Web of Science ®Google Scholar
• Nelson , W. 1990 . Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , New York : John Wiley .
   Google Scholar
• Ostrouchov , G. and Meeker , W. Q. 1988 . “Accuracy of Approximate Confidence Bounds Computed from Interval Censored Weibull and Lognormal Data” . Journal of Statistical Computation and Simulation , 29 : 43 – 76 .
   Google Scholar
• Rao , C. R. 1973 . Linear Statistical Inference and Its Applications , New York : John Wiley .
   Google Scholar
• Searle , S. R. , Casella , G. and McCulloch , C. E. 1992 . Variance Components , New York : John Wiley .
   Google Scholar
• Seber , G. A. F. and Wild , C. J. 1989 . Nonlinear Regression , New York : John Wiley .
   Google Scholar
• Severini , T. A. 1991 . “On the Relationship Between Bayesian and Non-Bayesian Interval Estimates” . Journal of the Royal Statistical Society , 53 : 611 – 618 . Ser. B
   Google Scholar
• Sprott , D. A. 1973 . “Normal Likelihoods and Their Relation to Large Sample Theory of Estimation” . Biometrika , 60 : 457 – 465 .
   Web of Science ®Google Scholar
• Sprott , D. A. 1975 . “Application of Maximum Likelihood Methods to Finite Samples” . Sankhyā , 37 : 259 – 270 .
   Google Scholar
• Sprott , D. A. 1980 . “Maximum Likelihood in Small Samples: Estimation in the Presence of Nuisance Parameters” . Biometrika , 67 : 515 – 523 .
   Web of Science ®Google Scholar
• Stuart , A. and Ord , K. 1991 . Kendall's Advanced Theory of Statistics, Volume 2: Classical Inference and Relationship, , 5th ed. , Oxford , , U.K. : Oxford University Press .
   Google Scholar
• Vander Wiel , S. A. and Meeker , W. Q. 1990 . “Accuracy of Approximate Confidence Bounds Using Censored Weibull Regression Data from Accelerated Life Tests” . IEEE Transactions on Reliability , 39 : 346 – 351 .
   Web of Science ®Google Scholar
• Venzon , D. J. and Moolgavkar , S. H. 1988 . “A Method of Computing Profile-Likelihood-Based Confidence Intervals” . Applied Statistics , 37 : 87 – 94 .
   Web of Science ®Google Scholar