(Received February 6, 1995; revised October 16, 1995)
Abstract. Let X=(X1, X2, ...., Xd)t be a random vector of positive entries, such that for some lambda = (lambda1, lambda2, ....., lambdad)t, the vector X(lambda) defined by Xi(lambdai) = (Xilambdai - 1)/lambdai, i = 1,....., d is elliptically symmetric. We describe a procedure based on the multivariate empirical characteristic function for estimating the lambdai's. Asymptotic results regarding consistency of the estimators are given and we evaluate their performance in simulated data. In a one-dimensional setting, comparisons are made with other available transformations to symmetry.
Key words and phrases: Elliptically contoured distributions, empirical characteristic function, Box-Cox transformations.