Anzeige
Erschienen in:
2007 | OriginalPaper | Buchkapitel
Nonstandard likelihood ratio test in exponential families
verfasst von : Jacques Bosgiraud
Erschienen in: The Strength of Nonstandard Analysis
Verlag: Springer Vienna
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by (Link öffnet in neuem Fenster)
Let (
p
θ
)
θ
∈Θ
be an exponential family in ℝ
k
. After establishing nonstandard results about large deviations of the sample mean
$$ \overline X $$
, this paper defines the nonstandard likelihood ratio test of the null hypothesis
H
0
: θ ∈ hal(
$$ \widetilde\Theta _0 $$
), where
$$ \widetilde\Theta _0 $$
is a standard subset of Θ and hal(
$$ \widetilde\Theta _0 $$
) its halo. If
α
is the level of the test, depending on whether ln
α
/
n
is infinitesimal or not we obtain different rejection criteria. We calculate risks of the first and second kinds (external probabilities) and prove that this test is more powerful than any “regular” nonstandard test based on
$$ \overline X $$
.
