Second order ancillary: A differential view from continuity

Bernoulli

Volumn 16, Issue 4, 2010, Pages 1208-1223

  Fraser, Ailana M ^a   Fraser, D A S ^b   Staicu, Ana Maria ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF TORONTO   (Canada)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Approximate ancillary; Approximate location model; Conditioning; Confidence; P value; Quantile

Indexed keywords

EID: 79251581581     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/10-BEJ248     Document Type: Article

References (29)

1. Andrews, D.F., Fraser, D.A.S. and Wong, A. (2005). Computation of distribution functions from likelihood information near observed data. J. Statist. Plann. Inference 134 180-193.
2. Barndorff-Nielsen, O.E. (1986). Inference on full or partial parameters based on the standardized log likelihood ratio. Biometrika 73 307-322.
3. Barndorff-Nielsen, O.E. (1987). Discussion of "Parameter orthogonality and approximate conditional inference." J. R. Stat. Soc. Ser. B Stat. Methodol. 49 18-20.
4. Berger, J.O. and Sun, D. (2008). Objective priors for the bivariate normal model. Ann. Statist. 36 963-982.
5. Cakmak, S., Fraser, D.A.S. and Reid, N. (1994). Multivariate asymptotic model: Exponential and location approximations. Util. Math. 46 21-31.
6. Cheah, P.K., Fraser, D.A.S. and Reid, N. (1995). Adjustment to likelihood and densities: Calculating significance. J. Statist. Res. 29 1-13.
7. Cox, D.R. (1980). Local ancillarity. Biometrika 67 279-286.
8. Cox, D.R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference. J. R. Stat. Soc. Ser. B Stat. Methodol. 49 1-39.
9. Daniels, H.E. (1954). Saddle point approximations in statistics. Ann. Math. Statist. 25 631-650.
10. Fisher, R.A. (1925). Theory of statistical estimation. Proc. Camb. Phil. Soc. 22 700-725.
11. Fisher, R.A. (1934). Two new properties of mathematical likelihood. Proc. R. Soc. Lond. Ser. A 144 285-307.
12. Fisher, R.A. (1935). The logic of inductive inference. J. R. Stat. Soc. Ser. B Stat. Methodol. 98 39-54.
13. Fisher, R.A. (1956). Statistical Methods and Scientific Inference. Edinburgh: Oliver & Boyd.
14. Fraser, D.A.S. (1979). Inference and Linear Models. New York: McGraw-Hill.
15. Fraser, D.A.S. (1993). Directional tests and statistical frames. Statist. Papers 34 213-236.
16. Fraser, D.A.S. (2003). Likelihood for component parameters. Biometrika 90 327-339.
17. Fraser, D.A.S. (2004). Ancillaries and conditional inference, with discussion. Statist. Sci. 19 333-369.
18. Fraser, D.A.S. and Reid, N. (1995). Ancillaries and third order significance. Util. Math. 47 33-53.
19. Fraser, D.A.S. and Reid, N. (2001). Ancillary information for statistical inference. In Empirical Bayes and Likelihood Inference (S.E. Ahmed and N. Reid, eds.) 185-207. New York: Springer.
20. Fraser, D.A.S. and Reid, N. (2002). Strong matching for frequentist and Bayesian inference. J. Statist. Plann. Inference 103 263-285.
21. Fraser, D.A.S., Reid, N., Marras, E. and Yi, G.Y. (2010). Default priors for Bayes and frequentist inference. J. R. Stat. Soc. Ser. B Stat. Methodol. To appear.
22. Fraser, D.A.S., Reid, N. and Wu, J. (1999). A simple general formula for tail probabilities for Bayes and frequentist inference. Biometrika 86 249-264.
23. Fraser, D.A.S. and Rousseau, J. (2008). Studentization and deriving accurate p-values. Biometrika 95 1-16.
24. Fraser, D.A.S.,Wong, A. andWu, J. (1999). Regression analysis, nonlinear or nonnormal: Simple and accurate p-values from likelihood analysis. J. Amer. Statist. Assoc. 94 1286-1295.
25. Lugannani, R. and Rice, S. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables. Adv. in Appl. Probab. 12 475-490.
26. McCullagh, P. (1984). Local sufficiency. Biometrika 71 233-244.
27. McCullagh, P. (1992). Conditional inference and Cauchy models. Biometrika 79 247-259.
28. Reid, N. and Fraser, D.A.S. (2010). Mean likelihood and higher order inference. Biometrika 97. To appear.
29. Severini, T.A. (2001). Likelihood Methods in Statistics. Oxford: Oxford Univ. Press.