Applications of the asymmetric eigenvalue problem techniques to robust testing

Citations of this article
Mendeley users who have this article in their library.
Get full text


To study the possibility of constructing a practical alternative to the computation of the p- values of the τ-test statistic, we study the properties of its asymptotic distribution. Using results from perturbation theory, we study the geometry of the matrix that governs the asymptotic distribution of the τ-test statistic. We consider the eigenvalues of this matrix as functions of the leverages, hi, i = 1,2,...,n, and we obtain power series expansions of the eigenvalues in terms of the factors hi-p/n, i = 1,2,..., n. From these expansions we see that it is precisely the high leverage cases that cause the eigenvalues to separate. Using Gerschgorin type theorems we try to group the eigenvalues into isolated discs. If the eigenvalues cannot be separated to different isolated discs, but all belong to overlapping discs, then they can be grouped in just one disc and be replaced by their average eigenvalue. In this case the p-value associated with the τ-test statistic can be approximated from the existing chisquare tables. © 1992.




Markatou, M., & Hettmansperger, T. P. (1992). Applications of the asymmetric eigenvalue problem techniques to robust testing. Journal of Statistical Planning and Inference, 31(1), 51–65.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free