Studentization and deriving accurate p-values

Biometrika

Volumn 95, Issue 1, 2008, Pages 1-16

  Fraser, D A S ^a   Rousseau, Judith ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Ancillary; Bayesian; Behrens Fisher problem; Bootstrap; Conditioning; Departure measure; Likelihood; P value; Studentization

Indexed keywords

EID: 40249114905     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asm093     Document Type: Article

References (24)

1. BARNDORFF-NIELSEN, O. E. (1986). Inference on full or partial parameters based on the standardised signed log likelihood ratio. Biometrika 73, 307-22.
2. BAYARRI, M. J. & BERGER, J. O. (2000). p-values for composite null models. J. Am. Statist. Assoc. 95, 1127-42.
3. BEHRENS, W. V. (1929). Ein Beitrag zur Fehlerbereichnung bei wenigen Beobachtungen. Landwirt. Jahr. 68, 807-37.
4. BERAN, R. J. (1988). Pre-pivoting test statistics: A bootstrap view of asymptotic refinements. J. Am. Statist. Assoc. 83, 687-97.
5. BHATTACHARYA, R. N. & GHOSH, J. K. (1978). On the validity of the formal Edgeworth expansion. Ann. Statist. 6, 434-51.
6. BICKEL, P. J. & GHOSH, J. K. (1990). A decomposition for the likelihood ratio statistic and the Bartlett correction - A Bayesian argument. Ann. Statist. 18, 1070-90.
7. BOX, G. E. P. (1980). Sampling and Bayes inference in scientific modelling (with Discussion). J. R. Statist. Soc. A 143, 383-430.
8. CAKMAK, S., FRASER, D. A. S., MCDUNNOUGH, P., REID, N. & YUAN, X. (1998). Likelihood centered asymptotic model: Exponential and location model versions. J. Statist. Plan. Infer. 66, 211-22.
9. CAKMAK, S., FRASER, D. A. S. & REID, N. (1994). Multivariate asymptotic model: Exponential and location approximations. Utilitas Math. 46, 21-31.
10. DAVISON, A. C., FRASER, D. A. S. & REID, N. (2006). Improved likelihood inference for discrete data. J. R. Statist. Soc. B 68, 495-508.
11. FISHER, R. A. (1935). The logic of inductive inference. J. R. Statist. Soc. 98, 39-54.
12. FRASER, D. A. S. (2003). Likelihood for component parameters. Biometrika 90, 327-39.
13. FRASER, D. A. S. (2004). Ancillaries and conditional inference (with Discussion). Statist. Sci. 19, 333-69.
14. FRASER, D. A. S. & REID, N. (1993). Third order asymptotic models: Likelihood functions leading to accurate approximations for distribution functions. Statist. Sinica 3, 67-82.
15. FRASER, D. A. S. & REID, N. (1995). Ancillaries and third order significance. Utilitas Math. 47, 330-53.
16. FRASER, D. A. S. & REID, N. (2001). Ancillary information for statistical inference. In Empirical Bayes and Likelihood Inference, Ed. S. E. Ahmed and N. Reid, pp. 185-207. New York: Springer-Verlag.
17. FRASER, D. A. S., REID, N. & WU, J. (1999). A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika 86, 249-64.
18. GELMAN, A., CARLIN, J. B., STERN, H. & RUBIN, D. B. (1995). Bayesian Data Analysis. London: Chapman and Hall.
19. GHOSH, M. & KIM, Y.-H. (2001). The Behrens-Fisher problem revisited: A Bayesian-frequentist synthesis. Can. J. Statist. 29, 5-17.
20. JEFFREYS, H. (1961). Theory of Probability, 3rd ed. Oxford: Oxford University Press.
21. LUGANNANI, R. & RICE, S. O. (1980). Saddlepoint approximation for the distribution of the sums of independent random variables. Adv. Appl. Prob. 12, 457-90.
22. ROBINS, J. M., VAN DER VAART, A. & VENTURA, V. (2000). The asymptotic distribution of p-values in composite null models. J. Am. Statist. Assoc. 95, 1143-56.
23. ROUSSEAU, J. (2007). Approximating interval hypotheses : p-values and Bayes factor. In Bayesian Statistics 8, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith., pp. 417-52. Oxford: Oxford University Press.
24. STUDENT (1908). The probable error of a mean. Biometrika 6, 1-25.