Asymptotic Methods in Statistical Inference - Statistics Centre

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5. Introduction to asymptotic tests
• General testing framework: We observe X =
( 1 ) where the distribution of X depends
on a (univariate) parameter . Wetest : = 0
vs. : 0 by rejecting if a ‘test statistic’
= (X) is too large, say ,the‘critical
value’ defining the ‘rejection region’. For a
specified ‘level’
= (Type I error) = (reject | true)
we wish to attain asymptotically:
0 ( )= + (1)