Locally Maximin Test for the Mixture Proportion with Type-I Censoring

Abstract

Mixtures of distributions arise frequently in the context of life testing experiments, where one also encounters the problem of censored data. In this article, we derive the locally most powerful (LMP) test for testing the mixing proportion in a general mixture model based on type-I censored data. We also prove the additional properties of unbiasedness and locally maximin using a novel approach. To this end, we prove an extension of a standard lemma in the testing literature (Lehmann, 1986) relating to families with monotone likelihood ratio.

Keywords:

• Locally most powerful tests
• Maximin tests
• MLR property
• Type-I censoring

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62N01, 62N03, 62N05