Abstract
The likelihood ratio principle. The development of a theory of hypothesis testing (as contrasted with the consideration of particular cases), may be said to have begun with the 1928 paper of Neyman and Pearson [16]. For in this paper the fundamental fact is pointed out that in selecting a suitable test one must take into account not only the hypothesis but also the alternatives against which the hypothesis is to be tested, and on this basis the likelihood ratio principle is proposed as a generally applicable criterion. This principle has proved extremely successful; nearly all tests now in use for testing parametric hypotheses are likelihood ratio tests, (for an extension to the non-parametric case see [33]), and many of them have been shown to possess various optimum properties.
Parts of this paper were presented in an invited address at the meeting of the Institute of Mathematical Statistics on Dec. 30, 1948, in Cleveland, Ohio.
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Lehmann, E.L. (2012). Some Principles of the Theory of Testing Hypotheses. 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_14
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