Testing Multivariate Symmetry
The paper presents a procedure for testing a general multivariate distribution for symmetry about a point and, also, a procedure adapted to the special properties of multivariate stable laws. In the general case use is made of a stochastic process derived from the empirical characteristic function. Under symmetry weak convergence to a Gaussian process is established and a test statistic is defined in terms of this limit process. Unlike circumstances in the univariate case, it is found convenient to estimate the center of symmetry and a spherically trimmed mean is used for that purpose. The procedure specifically concerned with multivariate stable laws is based on estimates of the spectral measure and index of stability. A numerical example concerning a bivariate distribution is given.
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Volume (Year): 54 (1995)
Issue (Month): 1 (July)
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