STATS 426 Lecture Notes - Lecture 9: Nuisance Parameter, Independent And Identically Distributed Random Variables, Random Variable
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In statistical jargon, the set of plausible values will be called a con dence set and the degree of plausibility will be called the level of con dence. For a small fraction (0. 01,0. 05,0. 1, typically), a level 1 con dence set for h( ) is de ned as any (random) subset of the real line, s(y ), say, such that. Thus, the con dence set itself will depend on the observed data y . Prob (h( ) s(y )) = 1 . Such a is called a pivot. (2) let g denote the distribution function of the pivot. The idea now is to get a range of plausible values of the pivot. The level of con dence 1 is to be used to get the appropriate range. This can be done in a variety of ways but the following is standard. Denote by q(g; ) the "th quantile of g. thus, Prob ( (y, h( )) q(g; )) = .