Statistique non Parametrique Asymptotique - download pdf or read online

By J.P. Raoult

ISBN-10: 3540102396

ISBN-13: 9783540102397

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Example text

Fisher made considerable use of likelihood and conditioning concepts (cf. Fisher (1925, 1934, 1956a)) and came close to espousing the LP in Fisher (1956a), but refrained from complete committment to the principle. Versions of the LP were developed and promoted by Barnard in a series of works (Barnard (1947a, 1947b, 1949)). Likelihood concepts were also employed by a number of other statisticians, cf. Bartlett (1936, 1953). The LP received major notice in 1962, due to Barnard, Jenkins, and Winsten (1962) and Birnbaum (1962a).

2 Axiomatic Development The formal statement of the LP is as follows. FORMAL LIKELIHOOD PRINCIPLE. Consider two experiments E, = {X,, θ, {f 1 }) and E« = (Xos θ» {fg})> where θ is the same quantity in each experiment. Suppose that for the particular realizations xί and x| from E, and E2» respectively, THE LIKELIHOOD PRINCIPLE AND GENERALIZATIONS 27 * xx* ( β ) = « x* ( θ ) 1 2 constant c ( i . e . , f Λ ( x ί ) = c f . (x£) / o r α Π θ ) . T/zerc E v ( E Γ x * ) = Ev(E2,x*). LIKELIHOOD PRINCIPLE COROLLARY.

X^ have been observed, and that v. ,n-l. (u ,n~ ) density. The LP thus says that the evidence about ξ is contained in I (ξ), and if we are stopping the experiment nothing else is needed. However, in deciding whether or not to take another observation, it is obvious that knowledge of v is crucial. If v = 1 it may be desirable to take another observation, but if v = 0 it would be a waste of time (since the measuring instrument is broken). This example is related to a limitation of sufficiency (cf.

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Statistique non Parametrique Asymptotique by J.P. Raoult

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