Optimal detection of Fechner-asymmetry

Journal of Statistical Planning and Inference

Volumn 138, Issue 8, 2008, Pages 2499-2525

  Cassart, Delphine ^a   Hallin, Marc ^a   Paindaveine, Davy ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Local asymptotic normality; Signed rank tests; Skewed densities; Tests for symmetry

Indexed keywords

EID: 42149174276     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.10.011     Document Type: Article

References (30)

1. Antille A. A linearized version of the Hodges-Lehmann estimator. Ann. Statist. 2 (1974) 1308-1313
2. Arellano-Valle R.B., Gómez H.W., and Quintana F.A. Statistical inference for a general class of asymmetric distributions. J. Statist. Plann. Inference 128 (2005) 427-443
3. Azzalini A., and Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65 (2003) 367-389
4. Beran R. Asymptotically efficient adaptive rank estimates in location models. Ann. Statist. 2 (1974) 63-74
5. Bickel P.J., and Ritov Y. Estimating integrated squared density derivatives. Sankhya Ser. A 50 (1988) 381-393
6. Butler C.C. A test for symmetry using the sample distribution function. Ann. Math. Statist. 40 (1969) 2209-2210
7. Cassart, D., Hallin, M., Paindaveine, D., 2007. A class of optimal tests for symmetry based on Edgeworth approximations, submitted for publication.
8. Cheng K.F., and Serfling R.J. On estimation of a class of efficiency-related parameters. Scand. Actuar. J. 8 (1981) 83-92
9. Fan J. On the estimation of quadratic functionals. Ann. Statist. 19 (1991) 1273-1294
10. Fechner G.T. Kollectivmasslehre (1897), Engleman, Leipzig
11. Hallin M., and Paindaveine D. Semiparametrically efficient rank-based inference for shape: I. Optimal rank-based tests for sphericity. Ann. Statist. 34 (2006) 2707-2756
12. Hallin M., and Werker B.J.M. Semiparametric efficiency, distribution-freeness, and invariance. Bernoulli 9 (2003) 137-165
13. Hallin M., Oja H., and Paindaveine D. Semiparametrically efficient rank-based inference for shape: II. Optimal R-estimation of shape. Ann. Statist. 34 (2006) 2757-2789
14. Hill D.L., and Rao P.V. Tests of symmetry based on Cramér-von Mises statistics. Biometrika 64 (1977) 489-494
15. Jurečková J., and Sen P.K. Robust Statistical Procedures: Asymptotics and Interrelations (1996), Wiley, New York
16. Koul, H.L., 2002. Weighted Empirical Processes in Dynamic Nonlinear Models, second ed., Springer, New York.
17. Kraft C.H., and van Eeden C. Linearized rank estimates and signed-rank estimates for the general linear hypothesis. Ann. Math. Statist. 43 (1972) 42-57
18. Kreiss J.-P. On adaptative estimation in stationary ARMA processes. Ann. Statist. 15 (1987) 112-133
19. Le Cam L.M. Asymptotic Methods in Statistical Decision Theory (1986), Springer, New York
20. Lehmann E.L. Nonparametric confidence intervals for a shift parameter. Ann. Math. Statist. 34 (1963) 1507-1512
21. McWilliams T.P. A distribution-free test for symmetry based on a runs statistic. J. Amer. Statist. Assoc. 85 (1990) 1130-1133
22. Puri M.L., and Sen P.K. Nonparametric Methods in General Linear Models (1985), Wiley, New York
23. Randles R.H., Fligner M.A., Policello G.E., and Wolfe D.A. An asymptotically distribution-free test for symmetry versus asymmetry. J. Amer. Statist. Assoc. 75 (1980) 168-172
24. Rothman E.D., and Woodrofe M. A Cramér-von Mises type statistic for testing symmetry. Ann. Math. Statist. 43 (1972) 2035-2038
25. Schweder T. Window estimation of the asymptotic variance of rank estimators of location. Scand. J. Stat. 2 (1975) 113-126
26. Sen P.K. On a distribution-free method of estimating asymptotic efficiency of a class of nonparametric tests. Ann. Math. Statist. 37 (1966) 1759-1770
27. Stein, C., 1956. Efficient nonparametric testing and estimation, in: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 187-196.
28. Stone C. Adaptive maximum likelihood estimation of a location parameter. Ann. Statist. 3 (1975) 267-284
29. Swensen A.R. The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. J. Multivariate Anal. 16 (1985) 54-70
30. Van Eeden C. An analogue, for signed-rank statistics, of Jurečková's asymptotic linearity theorem for rank statistics. Ann. Math. Statist. 43 (1972) 791-802