Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 91-112 |
Number of pages | 22 |
Journal | Journal of Multivariate Analysis |
Volume | 54 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1995 |
Keywords
- Center of symmetry
- Empirical characteristic function
- Multivariate stable laws
- Multivariate symmetry