JinSeo.Cho - Testing Hypotheses Using a Mixture of Null and Alternative Models

<Abstract> This study examines the testing of statistical hypotheses by forming a mixture of null and alternative models. The motivation for this model expansion stems from the concern that the null hypothesis may be rejected because the original model is misspecified. The likelihood-ratio (LR) test formed by the mixture requires non-standard analysis under the null because the model suffers from twofold identification and boundary parameter problems. We overcome these challenges and show that the null limit distribution of the LR test is represented as a functional of a Gaussian process. We illustrate the use of the LR test by assuming a popular linear model and demonstrate its usefulness by Monte Carlo simulations.