Principal investigator: James F. Troendle, Ph.D.
Methods of testing the Nonparametric Behrens-Fisher Hypothesis (NBFH) are studied. A generalized maximum likelihood estimator (GMLE) was found under the null hypothesis for this problem by numerically solving a single dimensional nonlinear equation. A generalized likelihood ratio test (GLRT) is then used to test the NBFH. The distribution of the test statistic can be approximated quite well by sampling from the constrained GMLE. The GLRT test has higher power than any existing method for this problem.

The above GLRT methodology can also be used when the data have right censoring. In this case, the method is applied to the data after the censored observations have been re-distributed to the right. Care must be taken so that if any maximum value is censored, it is re-distributed according to the null hypothesis. Special permutation methods can be used to approximate the distribution of the test statistic under the identity hypothesis. Sampling from the constrained GMLE works well to approximate the distribution under the NBFH.

Recent work indicates that a semiparametric model can be used to test the NBFH. The model can be made robust by allowing a Box-Cox type of transformation of the data.
 
DESPR Collaborators

· Kai Fun Yu, Ph.D.

Selected Publications

Troendle JF & Yu KF. (2006). Likelihood approaches to the nonparametric two-sample problem with right censored data. Statistics in Medicine, 25:2284-2298. [Abstract]

Fokianos K & Troendle JF. (In press). Inference for the relative treatment effect with the Density Ratio Model. Statistical Modeling: An International Journal.

Troendle JF. (2002). A likelihood ratio test for the Nonparametric Behrens-Fisher Problem. Biometrical Journal, 44:813-824.