ESTIMATION OF A MULTIVARIATE BOX-COX TRANSFORMATION TO ELLIPTIC SYMMETRY VIA THE EMPIRICAL CHARACTERISTIC FUNCTION

Let X = (X(1), X(2),..., X(d))(t) be a random vector of positive entri es, such that for some lambda = (lambda(1), lambda(2), lambda(d))(t), the vector X((lambda)) defined by X(i)((lambda i)) = (X(i)(lambda i) - 1)/lambda(i), i = 1,..., d is elliptically symmetric. We describe a p rocedure based on the multivariate empirical characteristic function f or estimating the lambda(i)'s. Asymptotic results regarding consistenc y of the estimators are given and we evaluate their performance in sim ulated data. In a one-dimensional setting, comparisons are made with o ther available transformations to symmetry.