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Inferential Models
book

Inferential Models

by Ryan Martin, Chuanhai Liu
September 2015
Intermediate to advanced content levelIntermediate to advanced
276 pages
9h 7m
English
Chapman and Hall/CRC
Content preview from Inferential Models
206 GENERALIZED INFERENTIAL MODELS
First, consider a hypothesis testing problem, H
0
: θ Θ
0
versus H
1
: θ 6∈ Θ
0
.
Define a plausibility function-based test as follows:
reject H
0
if and only if pl
y
(Θ
0
) α. (11.9)
The intuition is that if Θ
0
is not sufficiently plausible, given Y = y, then one should
conclude that the true θ is outside Θ
0
. An immediate consequence of Theorem 11.1
is that this test controls the probability of a Type I error at level α.
Corollary 11.1. For any α (0,1), the size of the test (11.9) is no more than α.
That is, sup
θΘ
0
P
θ
{pl
Y
(Θ
0
) α} α. Moreover, if H
0
is a point-null, so that Θ
0
is a singleton, and T
Y,θ
is a continuous random variable ...
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Publisher Resources

ISBN: 9781439886519