Local Bahadur efficiency of some goodness-of-fit tests under skew alternatives

Journal of Statistical Planning and Inference

Volumn 115, Issue 1, 2003, Pages 171-179

  Durio, A ^a   Nikitin, Ya Yu ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Bahadur efficiency; Kullback Leibler information; Local asymptotic optimality; Local index; Skew alternative

Indexed keywords

EID: 0038405129     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00155-6     Document Type: Article

References (25)

1. Abrahamson I.G. Exact Bahadur efficiencies for the Kolmogorov-Smirnov and Kuiper one- and two-sample statistics Ann. Math. Statist. 38 2 1967 1475-1490
2. Arnold B.C. Beaver R.J. The skew-Cauchy distribution Statist. Probab. Lett. 49 3 2000 285-290
3. Azzalini A. A class of distributions which includes the normal ones Scand. J. Statist. 12 1985 171-178
4. Azzalini A. Further results on a class of distributions which includes the normal ones Statistica 46 1986 199-208
5. Azzalini A. Capitanio A. Statistical applications of the multivariate normal skew distribution J. Roy. Statist. Soc., Ser. B 61 3 1999 579-602
6. Azzalini A. Dalla Valle A. The multivariate skew-normal distribution Biometrika 83 4 1996 715-726
7. Bahadur R.R. Rates of convergence of estimates and test statistics Ann. Math. Statist. 38 1967 303-324
8. Bahadur R.R. Some Limit Theorems in Statistics 1971 SIAM Philadelphia
9. Branco M.D. Dey D. A general class of multivariate skew-elliptical distributions J. Multivariate Anal. 79 1 2001 99-113
10. Chiogna M. Some results on the scalar skew-normal distribution J. Ital. Statist. Soc. 7 1998 1-13
11. Durio, A., Nikitin, Ya.Yu., 2001. Local asymptotic efficiency of some goodness-of-fit tests under skew alternatives. Working Paper No. 4/2001, International Centre for Economic Research (ICER), Torino, 18pp.
12. Genton M.G. He L. Liu X. Moments of skew-normal random vectors and their quadratic forms Statist. Probab. Lett. 51 2001 319-325
13. Groeneboom P. Shorack G. Large deviations of goodness-of-fit statistics and linear combinations of order statistics Ann. Probab. 9 1981 971-987
14. Henze N. A probabilistic representation of the 'skew-normal' distribution Scand. J. Statist. 13 1986 271-275
15. Johnson, N.L., Kotz, S., Read, C.B., 1988. Skew-normal distributions. In: Johnson, N.L., Kotz, S., Read, C.B. (Eds.), Encyclopedia of Statistical Sciences, Vol. 8. Wiley, New York, pp. 507-508.
16. Karlin S. Studden W.J. Tchebycheff systems: with Applications in Analysis and Statistics 1966 Wiley New York
17. Liseo B. The skew-normal class of densities: aspects of inference from the Bayesian point of view Statistica 50 l 1990 71-82
18. Nikitin Ya.Yu. Bahadur local asymptotic optimality and characterization problems Theory Probab. Appl. 29 1984 79-92
19. Nikitin Ya.Yu. Asymptotic Efficiency of Nonparametric Tests 1995 Cambridge University Press Cambridge
20. Norton R.M. Moment properties and the arcsine law Sankhya A 40 2 1978 192-198
21. Pewsey A. Problems of inference for Azzalini's skew-normal distribution J. Appl. Statist. 27 7 2000 859-870
22. Savage I.R. Nonparametric statistics: a personal review Sankhya A 31 1969 107 144
23. Shantaram R. A characterization of the arcsine law Sankhya A 40 2 1978 199-207
24. Shorack G. Wellner J. Empirical Processes with Applications to Statistics 1986 Wiley New York
25. Wieand H.S. A condition under which the Pitman and Bahadur approaches to efficiency coincide Ann. Statist. 4 1976 1003-1011