Abstract
In Part I of this study (Lehmann and Scheffé, I950), to which we shall refer as LSI, we defined and illustrated the ooncept of completeness of a family of measures and developed some of its statistical applications. In this part we shall state in section 7 some general results about complete families, showing how from given families one can construct others, and a specific result about the completeness of a certain parametric family. Uniformly most powerful, unbiased tests for certain statistical hypotheses about this parametric family are considered in section 8. Some examples are given in section 9. As mentioned2 in LSI, these results on testing are extensions and simplifications of earlier ones by Neyman (1941), Scheffé (1942), Lehmann (1947), Ghosh (1948), and Iioel (1948). Since then further papers have appeared on the subject by Nandi (1951) and Sverdrup (1953); however, the present version is in a number of ways more general than previous ones. The notation throughout will be that of LSI.
This papot• wns propo.rod with tho po.rtio.l support of the Office of Nn.vo.l Research, U.S.A.
Wo aho.ll not givo tho dl,rivn.t iou of tho solutions of tlur diffel•entinl equo.biona of Neymn.n o.nd Scheffè for tho po,rnmotrio fmnily of probability donaitiee, o.s nWl ounced in LSI, boco.usa this is lengthy, t-edious, and now muinly of historico.l interoet
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Lehmann, E.L., ScheffÉ, H. (2012). Completeness, Similar Regions, and Unbiased Estimation—Part II. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_24
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