Anomalies of the Likelihood Ratio Test for Testing Restricted Hypotheses

Abstract

The first anomaly in the L.R.T. for testing restricted hypotheses was observed by Warrack and Robertson. They found the L.R.T. for testing an order restriction in a normal model to be dominated by a different test. In this paper we deal with a more general situation in which the L. R. T. for testing a face of an acute cone is dominated by a different test that does not take into account some of the information in the model.