The Behrens-Fisher Problem: An Empirical Likelihood Ratio Approach

A new theoretical solution to the Behrens-Fisher (BF) problem is developed using empirical likelihood method. The sampling properties of the empirical likelihood ratio (ELR) test for the BF problem are derived using Monte Carlo simulation technique for a wide range of situations. A comparison of the size and power of the ELR test and the Welch-Aspin test is conducted for a special case of small sample sizes. The empirical results indicate that the ELR test for the BF problem has good power properties.