Is the locally best invariant test uniformly most powerful for a wider class of invariant tests?

Issue title: Estimation, Testing and Forecasting in Econometrics

Subtitle:

Guest editors: Jiti Gao and Maxwell L. King

Article type: Research Article

Authors: Bhowmik, J.L.

Affiliations: Department of Statistics, Data Science and Epidemiology, Faculty of Health, Arts and Design, Swinburne University of Technology, Melbourne, Victoria 3122, Australia. E-mail: [email protected]

Abstract: In the context of a general regression model in which some regression coefficients are of interest and others are purely nuisance parameters, Bhowmik and King [6] constructed the locally best invariant (LBI) test against one-sided alternatives. This paper investigates whether this LBI test is uniformly most powerful invariant (UMPI) or not through simulation results. A test that is locally best invariant against one-sided alternative hypotheses is found to be uniformly most powerful invariant (UMPI) in a wider class of tests than the invariant tests for the standard F test. The results of a simulation study conducted to prove that the LBI test is UMPI are presented. Through simulation results this study proves that the LBI test is UMPI.

Keywords: Invariant, simulation, one-sided testing, nuisance parameters, F test

DOI: 10.3233/MAS-150324

Journal: Model Assisted Statistics and Applications, vol. 10, no. 3, pp. 197-204, 2015