One-Sample Likelihood Ratio Tests for Mixed Data

Abstract

We revisit a hypothesis-testing problem recently investigated by de Leon and Carrière (2000). Specifically, we obtain exact likelihood ratio tests of one-sample location hypotheses for multivariate mixed data modeled according to the general location model (Olkin and Tate, 1961). The tests generalize those previously proposed by de Leon and Carrière (2000) for the case of mixed bivariate data. Optimal properties of the tests are briefly studied. Simulations show that the tests are reasonably powerful in detecting differences between the true and hypothesized populations. We illustrate the tests with a few examples, including one concerning data on academic achievement.

Keywords:

• General location model
• Level of test
• Location hypothesis
• Multi-nomial data
• Multivariate normal distribution
• Power function
• U-distribution
• Wishart distribution

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62H15

Acknowledgments

The author was supported by a Studentship Award from the Alberta Heritage Foundation for Medical Research (AHFMR) and by a grant from the Natural Sciences and Engineering Research Council of Canada. He is grateful to Yongtao Zhu for computational assistance and to the referee for very helpful comments which greatly improved the form and content of the article.

Notes

Figures in parentheses are theoretical power values, calculated from (5).