Summary
This paper is concerned with an extension of the problem of testing symmetry about zero of a distribution function. In order to obtain the asymptotic null distribution of test statistics for the problem, a limit theorem is proved, which indeed plays an essential role in the asymptotic theory of testing, problem for symmetry.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bickel, P. J. and Wichura, M. J. (1971). Convergence criteria for multiparameter stochastic process and some applications,Ann. Math. Statist.,42, 1656–1670.
Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.
Butler, C. (1969). A test for symmetry using the sample distribution function.,Ann. Math. Statist.,40, 2209–2210.
Feller, W. (1966).An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York.
Rothman, E. D. and Woodroofe, M. (1972). A Cramér-von Mises, type statistic for testing symmetry,Ann. Math. Statist.,43, 2035–2038.
Additional information
The Institute of Statistical Mathematics
About this article
Cite this article
Aki, S. On nonparametric tests for symmetry. Ann Inst Stat Math 39, 457–472 (1987). https://doi.org/10.1007/BF02491482
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02491482