The p-value Function and Statistical Inference

References

• Abe, F. (1994), “Evidence for Top Quark Production in pøp Collisions at Ãs =1.8 tev,” Physics Review Letters, 69, 033002.
   Google Scholar
• Banff International Research Station (2006), “Statistical Inference Problems in High Energy Physics and Astronomy,” available at https://www.birs.ca/events/2006/5-day-workshops/06w5054.
   Google Scholar
• Barndorff-Nielsen, O. E. (1983), “On a Formula for the Distribution of the Maximum Likelihood Estimate,” Biometrika, 70, 343–365. DOI: 10.1093/biomet/70.2.343.
   Web of Science ®Google Scholar
• Box, G., and Cox, D. (1964), “An Analysis of Transformations” (with discussions), Journal of Royal Statistical Society, Series B, 26, 211–252. DOI: 10.1111/j.2517-6161.1964.tb00553.x.
   Google Scholar
• Brazzale, A. R., Davison, A. C., and Reid, N. (2007). Applied Asymptotics Case Studies in Small-Sample Statistics, Cambridge, UK: Cambridge University Press.
   Google Scholar
• Brown, B. (1980), “Prediction Analysis for Binary Data,” in Biostatistics Casebook, eds. B. W. B. R. G. Miller, B. Efron, and L. E. Moses, New York: Wiley, pp. 3–18.
   Google Scholar
• Chen, G., Lockhart, R., and Stephens, M. (2002), “Box–Cox Transformations in Linear Models: Large Sample Theory and Tests of Normality,” Canadian Journal of Statistics, 30, 177–234. DOI: 10.2307/3315946.
   Web of Science ®Google Scholar
• Cox, D. R. (1958), “So+-me Problems Connected With Statistical Inference,” Annals of Mathematical Statistics, 29, 357–372. DOI: 10.1214/aoms/1177706618.
   Google Scholar
• Creasy, M. (1954), “Limits for the Ratios of Means,” Journal of Royal Statistical Society B, 16, 186–194. DOI: 10.1111/j.2517-6161.1954.tb00160.x.
   Google Scholar
• Daniels, H. E. (1954), “Saddlepoint Approximations in Statistics,” Annals of Mathematical Statistics, 46, 21–31.
   Google Scholar
• Davison, A., Fraser, D., and Reid, N. (2006), “Improved Likelihood Inference for Discrete Data,” Journal of Royal Statistical Society, Series B, 68, 495–508. DOI: 10.1111/j.1467-9868.2006.00548.x.
   Google Scholar
• Davison, A. C., and Sartori, N. (2008), “The Banff Challenge: Statistical Detection of a Noisy Signal,” Statistical Science, 23, 354–364. DOI: 10.1214/08-STS260.
   Web of Science ®Google Scholar
• Fieller, E. (1954), “Some Problems in Interval Estimation,” Journal of Royal Statistical Society, Series B, 16, 175–185. DOI: 10.1111/j.2517-6161.1954.tb00159.x.
   Google Scholar
• Fisher, R. (1922), “On the Mathematical Foundations of Theoretical Statistics,” Philosophical Transaction of Royal Society A, 222, 309–368. DOI: 10.1098/rsta.1922.0009.
   Google Scholar
• Fisher, R. (1930), “Inverse Probability,” Proceedings of the Cambridge Philosophical Society, 26, 528–535. DOI: 10.1017/S0305004100016297.
   Google Scholar
• Fraser, D., Reid, N., and Lin, W. (2018), “When Should Modes of Inference Disagree? Some Simple But Challenging Examples,” Annals of Applied Statistics, 12, 750–770. DOI: 10.1214/18-AOAS1160SF.
   Web of Science ®Google Scholar
• Fraser, D., Wong, A., and Sun, Y. (2009), “Three Enigmatic Examples and Inference From Likelihood,” Canadian Journal of Statistics, 37, 161–181. DOI: 10.1002/cjs.10008.
   Web of Science ®Google Scholar
• Fraser, D., Wong, A., and Wu, J. (2004), “Simple Accurate and Unique: The Methods of Modern Likelihood Theory,” Pakistan Journal of Statistics, 20, 173–192.
   Google Scholar
• Fraser, D. A. S. (2017), “The p-value Function: The Core Concept of Modern Statistical Inference,” Annual Review of Statistics and its Application, 4, 153–165. DOI: 10.1146/annurev-statistics-060116-054139.
   Web of Science ®Google Scholar
• Fraser, D. A. S., Reid, N., and Wong, A. (1997), “Simple and Accurate Inference for the Mean of the Gamma Model,” Canadian Journal of Statistics, 25, 91–99. DOI: 10.2307/3315359.
   Web of Science ®Google Scholar
• Fraser, D. A. S., Reid, N., and Wong, A. (2004), “On Inference for Bounded Parameters,” Physics Review D, 69, 033002.
   Web of Science ®Google Scholar
• Fraser, D. A. S., Reid, N., and Wong, A. (2009), “What a Model With Data Says About Theta,” International Journal of Statistical Science, 3, 163–177.
   Google Scholar
• Fraser, D. A. S., Reid, N., and Wu, J. (1999), “A Simple General Formula for Tail Probabilities for Frequentist and Bayesian Inference,” Biometrika, 86, 249–264. DOI: 10.1093/biomet/86.2.249.
   Web of Science ®Google Scholar
• Frome, E. L. (1983), “The Analysis of Rates Using Poisson Regression Models,” Biometrics, 39, 665–674. DOI: 10.2307/2531094.
   PubMed Web of Science ®Google Scholar
• Grice, J., and Bain, L. (1980), “Inference Concerning the Mean of the Gamma Distribution,” Journal of American Statistical Association., 75, 929–933. DOI: 10.1080/01621459.1980.10477574.
   Web of Science ®Google Scholar
• Gross, A., and Clark, V. (1975), Survival Distributions: Reli-ability Applications in the Biomedical Sciences. New York: Wiley.
   Google Scholar
• Neyman, J., and Pearson, E. S. (1933), “On the Problem of the Most Efficient Tests of Statistical Hypotheses,” Philosophical Transaction of Royal Society A, 231, 694–706.
   Google Scholar
• Reid, N., and Fraser, D. A. S. (2010), “Mean Likelihood and Higher Order Approximations,” Biometrika, 97, 159–170. DOI: 10.1093/biomet/asq001.
   Web of Science ®Google Scholar
• Rozeboom, W. (1960), “The Fallacy of the Null-Hypothesis Significance Test,” Psychological Bulletin, 57, 416–428.
   PubMed Web of Science ®Google Scholar
• Sartori, N., Fraser, D., and Reid, N. (2016), “Accurate Directional Inference for Vector Parameters,” Biometrika, 103, 625–639. DOI: 10.1093/biomet/asw022.
   Web of Science ®Google Scholar
• Sterling, T. D. (1959), “Publication Decisions and Their Possible Effects on Inferences Drawn From Tests of Significance—or Vice Versa,” Journal of American Statistical Association, 54, 30–34. DOI: 10.2307/2282137.
   Web of Science ®Google Scholar
• Wasserstein, R., and Lazar, N. (2016), “The ASA’s Statement on p-values: Context, Process, and Purpose,” The American Statistician, 70, 129–133. DOI: 10.1080/00031305.2016.1154108.
   Web of Science ®Google Scholar