Scale-invariant test of normality based on Polya's characterization

Metron

Volumn 60, Issue 1-2, 2002, Pages 21-33

  Muliere, P ^a   Nikitin, Ya ^b  

^a BOCCONI UNIVERSITY   (Italy)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Bahadur efficiency; Characterization of normality; Skew normal distribution; U statistics

Indexed keywords

EID: 19744366490     PISSN: 00261424     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. Ahmad, I. and Alwasel, I. (1999) A goodness-of-fit test for exponentiality based on the memoryless property, J.R. Statist. Soc., B61, Pt.3, 681-689.
2. Angus, J.E. (1982) Goodness-of-fit tests for exponentiality based on a loss-of-memory type functional equation, Journ. Statist. Plann. Inference, 6, 241-251.
3. Azzalini, A. (1985) A class of distributions which includes the normal ones, Scand. J. Stat., 12, 171-178.
4. Azzalini, A. and Dalla Valle, A. (1996) The multivariate skew-normal distribution, Biometrika, 83, 715-726.
5. Bahadur, R.R. (1960) Stochastic comparison of tests, Ann. Math. Stat., 31, 276-295.
6. Baringhaus, L. and Henze, N. (1992) A characterization of and new consistent tests of symmetry, Commun. Statist. Theor. Meth., 21, 1555-1566.
7. Bryc, W. (1995) Normal Distribution: Characterization with Applications, Lecture Notes in Statistics, vol. 100, Springer, Berlin.
8. Chiogna, M. (1998) Some results on the scalar skew-normal distribution, J. Ital. Statist. Soc., 7, 1-13.
9. Durio, A. and Nikitin, Ya.Yu. (2001) Local asymptotic efficiency of some goodnessof- fit tests under skew alternative, Submitted to publication.
10. Eichelsbacher, P. and Loewe, M. (1995) A large deviation principle for m-variate von Mises-statistics and U-statistics, J. of Theor. Prob., 8, 807-824.
11. Henze, N. (1986)Aprobabilistic representation of the "skew- normal" distribution, Scand. J. Stat., 13, 271-275.
12. Hettmansperger, T. (1984) Statistical Inference Based on Ranks, Wiley, New York.
13. Hollander, M. and Proschan, F. (1972) Testing whether new is better than used, Ann. Math. Stat., 43, 1136-1146.
14. Huber, P.J. (1981) Robust Statistics, Wiley, New York.
15. Janssen, P.L. (1988) Generalized Empirical Distribution Functions with Statistical Applications, Limburgs Universitair Centrum, Diepenbeek.
16. Kagan, A.M., Linnik, Yu.V., and Rao, C.R. (1973) Characterization Theorems of Mathematical Statistics, Wiley, New York.
17. Korolyuk, V.S. and Borovskikh, Yu.V. (1994) Theory of U-statistics, Kluwer, Dordrecht.
18. Koul, H.L. (1977) A test for new better than used, Commun.Statist. Theory Meth., A6, 563-574.
19. Mathai, A.M. and Pederzoli, G. (1977) Characterizations of the Normal Probability Law, Wiley, New York.
20. Nikitin, Ya. (1995) Asymptotic Efficiency of Nonparametric Tests, Cambridge University Press.
21. Nikitin, Ya. and Ponikarov E.V. (1999a) Large deviations of Chernoff type for Ustatistics and von Mises functionals, Proc. of St. Petersburg Math. Soc., 7, 124- 167, in Russian. To be translated by Amer. Math. Soc.
22. Nikitin, Ya. and Ponikarov E.V. (1999b) Large deviations of Chernoff type for U- and V-statistics, Doklady RAN, 369, 13-16.
23. Pewsey, A. (2000) Problems of inference for Azzalini's skew-normal distribution, J. of Appl. Stat., 27, 859-870.
24. Polya, G.(1923) Herleitung des Gauss'schen Fehlergesetzes aus einer Funktionsalsgleichung, Math. Zeitschrift, 18, 96-108.
25. Rao, C.R. (1965) Linear Statistical Inference and its Applications, Wiley, New York.
26. Serfling, R.J. (1980) Approximation Theorems of Mathematical Statistics, Wiley, New York.
27. Shapiro, S.S. and Wilk M.B. (1965) An analysis of variance test for normality (complete samples), Biometrika, 52, 591-611.
28. Stephens, M.A. (1974) EDF statistics for goodness of fit and some comparisons, Journ. Amer. Stat. Ass., 69, 730-737.
29. Tukey, J.W.(1960) A survey of sampling from contaminated distributions, In: Contributions to Probability and Statistics, Olkin,I. et al., eds, (Stanford University Press), 448-485.
30. Wieand, H.S. (1976) A condition under which the Pitman and Bahadur approaches to efficiency coincide, Ann. Statist., 4, 1003-1011.