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

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Rare event analysis for minimum Hellinger distance estimators via large deviation theory. / Vidyashankar, Anand N.; Collamore, Jeffrey F.

I: Entropy, Bind 23, Nr. 4, 386, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Vidyashankar, AN & Collamore, JF 2021, 'Rare event analysis for minimum Hellinger distance estimators via large deviation theory', Entropy, bind 23, nr. 4, 386. https://doi.org/10.3390/e23040386

APA

Vidyashankar, A. N., & Collamore, J. F. (2021). Rare event analysis for minimum Hellinger distance estimators via large deviation theory. Entropy, 23(4), [386]. https://doi.org/10.3390/e23040386

Vancouver

Vidyashankar AN, Collamore JF. Rare event analysis for minimum Hellinger distance estimators via large deviation theory. Entropy. 2021;23(4). 386. https://doi.org/10.3390/e23040386

Author

Vidyashankar, Anand N. ; Collamore, Jeffrey F. / Rare event analysis for minimum Hellinger distance estimators via large deviation theory. I: Entropy. 2021 ; Bind 23, Nr. 4.

Bibtex

@article{3260ae5d50104173adef4231b9405735,
title = "Rare event analysis for minimum Hellinger distance estimators via large deviation theory",
abstract = "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 propertiesof the affinity, which may be of independent interest.",
author = "Vidyashankar, {Anand N.} and Collamore, {Jeffrey F.}",
year = "2021",
doi = "10.3390/e23040386",
language = "English",
volume = "23",
journal = "Entropy",
issn = "1099-4300",
publisher = "MDPI AG",
number = "4",

}

RIS

TY - JOUR

T1 - Rare event analysis for minimum Hellinger distance estimators via large deviation theory

AU - Vidyashankar, Anand N.

AU - Collamore, Jeffrey F.

PY - 2021

Y1 - 2021

N2 - 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 propertiesof the affinity, which may be of independent interest.

AB - 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 propertiesof the affinity, which may be of independent interest.

U2 - 10.3390/e23040386

DO - 10.3390/e23040386

M3 - Journal article

C2 - 33805183

VL - 23

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 4

M1 - 386

ER -

ID: 257193238