Rare event analysis for minimum Hellinger distance estimators via large deviation theory

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Dokumenter

Hellinger distance has been widely used to derive objective functions that are alternatives to maximum likelihood methods. While the asymptotic distributions of these estimators have been well investigated, the probabilities of rare events induced by them are largely unknown. In this article, we analyze these rare event probabilities using large deviation theory under a potential model misspecification, in both one and higher dimensions. We show that these probabilities decay exponentially, characterizing their decay via a \rate function," which is expressed as a convex conjugate of a limiting cumulant generating function. In the analysis of the lower bound, in particular, certain geometric considerations arise which facilitate an explicit representation, also in the case when the limiting generating function is non-differentiable. Our analysis also involves the modulus of continuity properties
of the affinity, which may be of independent interest.
OriginalsprogEngelsk
TidsskriftEntropy
Vol/bind23
Udgave nummer4
Antal sider20
ISSN1099-4300
StatusUdgivet - 22 feb. 2021

Links

Antal downloads er baseret på statistik fra Google Scholar og www.ku.dk


Ingen data tilgængelig

ID: 257193238