Improved confidence regions based on Edgeworth expansions

Computational Statistics and Data Analysis

Volumn 56, Issue 12, 2012, Pages 4366-4380

  Withers, Christopher S ^a   Nadarajah, Saralees ^b  

^a CALLAGHAN INNOVATION   (New Zealand)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Cumulants; Edgeworth expansions; Ellipsoidal confidence regions

Indexed keywords

CONFIDENCE REGION; CUMULANT EXPANSION; CUMULANTS; EDGEWORTH EXPANSION;

STATISTICS;

EXPANSION;

EID: 84864143582     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.03.019     Document Type: Article

References (26)

1. L. Amendola Non-Gaussian likelihood function Astrophysical Letters and Communications 33 1996 63 69
2. L. Amendola Non-Gaussian likelihood function and COBE data Monthly Notices of the Royal Astronomical Society 283 1996 983 989
3. A. Azzalini, and A. Capitanio Statistical applications of the multivariate skew-normal distribution Journal of the Royal Statistical Society, B 61 1999 579 602
4. A. Azzalini, and A. Dalla Valle The multivariate skew-normal distribution Biometrika 83 1996 715 726
5. R.N. Bhattacharya, and R.R. Rao Normal Approximation and Asymptotic Expansion 1976 John Wiley and Sons New York
6. C.T. Chiang, S.H. Wang, and H. Hung Random weighting and Edgeworth expansion for the nonparametric time-dependent AUC estimator Statistica Sinica 19 2009 969 979
7. E.A. Cornish, and R.A. Fisher Moments and cumulants in the specification of distributions Revue de l'Institut Internat de Statistics 5 1937 307 322 Reproduced in The Collected Papers of R.A. Fisher, volume 4
8. H. Cramer Mathematical Methods of Statistics 1946 Princeton University Press Princeton
9. G.S. Datta, and R. Mukerjee Probability Matching Priors: Higher Order Asymptotics 2004 Springer Verlag New York
10. F. Götze, and R. Zitikis Edgeworth expansions and bootstrap for degenerate von Mises statistics. Dedicated to the memory of Jerzy Neyman Probability and Mathematical Statistics 15 1995 327 351
11. A. Guillou, and F. Merlevéde Second-order properties of the blocks of blocks bootstrap for density estimators for continuous time processes Mathematical Methods in Statistics 12 2003 1 30
12. P. Hall The Bootstrap and Edgeworth Expansion 1992 Springer Verlag New York
13. M.G. Kendall, and A. Stuart The Advanced Theory of Statistics, Volume I: Distribution Theory third ed. 1969 Charles Griffin and Company Limited London
14. J.F. Kenney, and E.S. Keeping Mathematics of Statistics, Part II second ed. 1959 D. Van Nostrand Company New York
15. S. Kotz, and S. Nadarajah Multivariate t Distributions and Their Applications 2004 Cambridge University Press New York
16. R.H. Myers, D.C. Montgomery, and C.M. Anderson-Cook Response Surface Methodology: Process and Product Optimization using Designed Experiments third ed. 2009 John Wiley and Sons Hoboken, New Jersey
17. V.V. Petrov Limit Theorems of Probability Theory: Sequences of Independent Random Variables 1995 Clarendon Press Oxford
18. D. Sengupta, and S.R. Jammalamadaka Linear Models: An Integrated Approach 2003 World Scientific Publishing Company River Edge, New Jersey
19. J.Y. Sun, C. Loader, and W.P. McCormick Confidence bands in generalized linear models Annals of Statistics 28 2000 429 460
20. E. Uusipaikka Confidence Intervals in Generalized Regression Models 2009 CRC Press Boca Raton, Florida
21. J. Vrbik Confidence regions based on Edgeworth expansion Communications in Statistics - Simulation and Computation 38 2009 1004 1018
22. C.S. Withers Expansions for the distribution and quantiles of a regular functional of the empirical distribution with applications to nonparametric confidence intervals Annals of Statistics 11 1983 577 587
23. C.S. Withers Nonparametric confidence intervals for functions of several distributions Annals of the Institute of Statistical Mathematics 40 1988 727 746
24. C.S. Withers The distribution and quantiles of a function of parameter estimates Annals of the Institute of Statistical Mathematics 34 A 1982 55 68
25. Withers, C.S.; Nadarajah, S.; 2011. Confidence intervals for linear combinations of Poisson means. Australian and New Zealand Journal of Statistics (in press).
26. J. Xu, and A.K. Gupta Improved confidence regions for a mean vector under general conditions Computational Statistics and Data Analysis 51 2006 1051 1062