Contributions to the Theory of Optimal Tests
AbstractThis paper considers tests which maximize the weighted average power(WAP). The focus is on determining WAP tests subject to an uncountablenumber of equalities and/or inequalities. The unifying theory allows us toobtain tests with correct size, similar tests, and unbiased tests, among others.A WAP test may be randomized and its characterization is not alwayspossible. We show how to approximate the power of the optimal test bysequences of nonrandomized tests. Two alternative approximations are considered.The rst approach considers a sequence of similar tests for an increasingnumber of boundary conditions. This discretization allows us toimplement the WAP tests in practice. The second method nds a sequenceof tests which approximate the WAP test uniformly. This approximationallows us to show that WAP similar tests are admissible.The theoretical framework is readily applicable to several econometricmodels, including the important class of the curved-exponential family. Inthis paper, we consider the instrumental variable model with heteroskedasticand autocorrelated errors (HAC-IV) and the nearly integrated regressormodel. In both models, we nd WAP similar and (locally) unbiased testswhich dominate other available tests.
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Bibliographic InfoPaper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 747.
Date of creation: 28 Oct 2013
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