High-order asymptotic expansions for robust tests

Biometrika

Volumn 88, Issue 4, 2001, Pages 1153-1168

  De Rossi, François Xavier ^a   Gatto, Riccardo ^b  

^a Swiss Federal Statistical Office   (Switzerland)

^b UNIVERSITY OF BERN   (Switzerland)

Author keywords

Bartlett correction; Edgeworth approximation; Likelihood ratio test; M ratio test; Nuisance parameter; Regression model; Robust p value and quantile; Saddlepoint approximation; Signed root likelihood ratio test; Signed root M ratio test

Indexed keywords

EID: 11844268846     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/88.4.1153     Document Type: Article

References (23)

1. ANDREWS, D. F. & STAFFORD, J. E. (1993). Tools for the symbolic computation of asymptotic expansions. J. R. Statist. Soc. B 55, 613-27.
2. BARNDORFF-NIELSEN, O. E. (1991). Modified signed log likelihood ratio. Biometrika 78, 557-63.
3. BARTLETT, M. S. (1937). Properties of sufficiency and statistical tests. Proc. R. Soc. Lond. A 160, 268-82.
4. BEDNARSKI, T. (1993). Predict differentiability of statistical functionals and implications to robust statistics. In New Directions in Statistical Data Analysis and Robustness, Ed. S. Morgenthaler, E. Ronchetti and W. A. Stahel, pp. 26-34. Berlin: Birkhäuser.
5. BHATTACHARYA, R. N. & GHOSH, J. K. (1978). On the validity of the formal Edgeworth expansion. Ann. Statist. 6, 434-51.
6. CLARKE, B. R. (1983). Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations. Ann. Statist. 11, 1196-205.
7. CLARKE, B. R. (1986). Non-smooth analysis and Fréchet differentiability of M-functionals. Prob. Theory Rel. Fields 73, 197-209.
8. DICICCIO, T. J. (1984). On parameter transformation and interval estimation. Biometrika 71, 477-85.
9. DICICCIO T. J. & MARTIN, M. A. (1993). Simple modifications for signed roots of likelihood ratio statistics. J. R. Statist. Soc. B 55, 305-16.
10. EASTON, G. S. & RONCHETTI, E. (1986). General saddlepoint approximations with applications to L statistics. J. Am. Statist. Assoc. 81, 420-30.
11. FAN, R. Y. K. & FIELD, C. A. (1995). Approximations for marginal densities of M-estimators. Can. J. Statist. 23, 185-97.
12. FIELD, C. A. & TINGLEY, M. A. (1997). Small sample asymptotics: applications in robustness. In Handbook of Statistics, 15, Ed. G. S. Maddala and C. R. Rao, pp. 513-36. Amsterdam: North Holland.
13. GATTO, R. & RONCHETTI, E. (1996). General saddlepoint approximations of marginal densities and tail probabilities. J. Am. Statist. Assoc. 91, 666-73.
14. HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. & STAHEL, W. A. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: Wiley and Sons.
15. HERITIER, S. & RONCHETTI, E. (1994). Robust bounded-influence tests in general parametric models. J. Am. Statist. Assoc. 89, 897-904.
16. HUBER, P. J. (1981). Robust Statistics. New York: Wiley and Sons.
17. LAWLEY, D. N. (1956). A general method for approximating to the distribution of likelihood ratio criteria. Biometrika 43, 295-303.
18. MARKATOU, M. & RONCHETTI, E. (1997). Robust inference: the approach based on influence functions. In Handbook of Statistics, 15, Ed. G. S. Maddala and C. R. Rao, pp. 49-75. Amsterdam: North Holland.
19. MCCULLAGH, P. (1987). Tensor Methods in Statistics. London: Chapman and Hall.
20. MCCULLAGH, P. & COX, D. R. (1986). Invariants and likelihood ratio statistics. Ann. Statist. 14, 1419-30.
21. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. New York: Wiley and Sons.
22. WANG, S. (1992). General saddlepoint approximations in the bootstrap. Statist. Prob. Lett. 13, 61-6.
23. WANG, S. (1995). One-step saddlepoint approximations for quantiles. Comp. Statist. Data Anal. 20, 65-74.