Rare Event Analysis for Minimum Hellinger Distance Estimators via Large Deviation Theory
| Autor: | Jeffrey F. Collamore, Anand N. Vidyashankar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Hellinger distance
General Physics and Astronomy lcsh:Astrophysics divergence measures 01 natural sciences Modulus of continuity Article large deviations 010305 fluids & plasmas 010104 statistics & probability 0103 physical sciences lcsh:QB460-466 Rare events Applied mathematics 0101 mathematics Convex conjugate lcsh:Science Generating function (physics) Mathematics rare event probabilities Estimator lcsh:QC1-999 Large deviations theory lcsh:Q Rate function lcsh:Physics |
| Zdroj: | Entropy Entropy, Vol 23, Iss 386, p 386 (2021) Vidyashankar, A N & Collamore, J F 2021, ' Rare event analysis for minimum Hellinger distance estimators via large deviation theory ', Entropy, vol. 23, no. 4, 386 . https://doi.org/10.3390/e23040386 Volume 23 Issue 4 |
| ISSN: | 1099-4300 |
| DOI: | 10.3390/e23040386 |
| Popis: | 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 that facilitate an explicit representation, also in the case when the limiting generating function is nondifferentiable. Our analysis involves the modulus of continuity properties of the affinity, which may be of independent interest. |
| Databáze: | OpenAIRE |
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