Summary
This paper investigates sequences of asymptotically similar critical regions {S n >0},n∈ℕ, under the assumption that the test-statisticS n admits a certain stochastic expansion. It is shown that for such test-sequences, first order efficiency implies second order efficiency (i.e. efficiency up to an error termo(n −1/2)). Moreover, the asymptotic power functions of first order efficient test-sequences are determined up to an error termo(n −1), and a class of critical regions is specified which is minimal essentially complete up too(n −1).
The results of this paper rest upon the technique of Edgeworth-expansions and are, therefore, restricted to “continuous” probability distributions.
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Pfanzagl, J., Wefelmeyer, W. An asymptotically complete class of tests. Z. Wahrscheinlichkeitstheorie verw Gebiete 45, 49–72 (1978). https://doi.org/10.1007/BF00635963
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DOI: https://doi.org/10.1007/BF00635963