Locally optimal test for simultaneously testing the mean and variance of a normal distribution |
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Authors: | Ashis Sen Gupta Lea Vermeire |
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Affiliation: | 1. Statistics &2. Applied Probability Program , University of California , Calcutta - INDIA, Santa Barbara, CA, 93106, USAIndian Statistical Institute;3. Department of Mathematics , Catholic University of Leuven , Campus Kortrijk, Kortrijk, B8500, Belgium |
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Abstract: | A generalization of the locally most powerful unbiased (LMPU) test for the single parameter case to the k-parameter case was proposed by SenGupta and Vermeire (1986). In particular we defined a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared to the type C tests of Neyman and Pearson and the type D tests (Isaacson, 1951), LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions. In this paper we present an interesting example of a two-parameter univariate normal population for which Isaacson (1951, p. 233) was unsuccessful in finding a type D test. For the case of one observation, we prove that no Type D region exists but the LMMPU test is obtained - it is an example of a test with singular Hessian matrix for its power but is nevertheless a strictly locally unbiased (LU) test. |
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Keywords: | Locally most mean power unbiased tests mean curvature |
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