On nonparametric tests for symmetry

  • Sigeo Aki


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.

Key words and phrases

Wiener process empirical distribution goodness-of-fit test test for symmetry weak convergence 


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  1. [1]
    Bickel, P. J. and Wichura, M. J. (1971). Convergence criteria for multiparameter stochastic process and some applications,Ann. Math. Statist.,42, 1656–1670.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.zbMATHGoogle Scholar
  3. [3]
    Butler, C. (1969). A test for symmetry using the sample distribution function.,Ann. Math. Statist.,40, 2209–2210.CrossRefGoogle Scholar
  4. [4]
    Feller, W. (1966).An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York.zbMATHGoogle Scholar
  5. [5]
    Rothman, E. D. and Woodroofe, M. (1972). A Cramér-von Mises, type statistic for testing symmetry,Ann. Math. Statist.,43, 2035–2038.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1987

Authors and Affiliations

  • Sigeo Aki

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