International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 249564, 7 pages
Research Article

The Laplace Likelihood Ratio Test for Heteroscedasticity

Department of Mathematical Statistics and Actuarial Science, University of the Free State, P.O. Box 339, Bloemfontein 9300, South Africa

Received 1 December 2010; Accepted 7 April 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 J. Martin van Zyl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is shown that the likelihood ratio test for heteroscedasticity, assuming the Laplace distribution, gives good results for Gaussian and fat-tailed data. The likelihood ratio test, assuming normality, is very sensitive to any deviation from normality, especially when the observations are from a distribution with fat tails. Such a likelihood test can also be used as a robust test for a constant variance in residuals or a time series if the data is partitioned into groups.