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  4. Higher-order infinitesimal robustness
 
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Higher-order infinitesimal robustness

Journal
Journal of the American Statistical Association : JASA
ISSN
0162-1459
ISSN-Digital
1537-274X
Type
journal article
Date Issued
2012-12-21
Author(s)
La Vecchia, Davide  
Ronchetti, Elvezio
Trojani, Fabio
DOI
10.1080/01621459.2012.738580
Abstract
Using the von Mises expansion, we study the higher-order infinitesimal robustness of a general M-functional and characterize its second-order properties. We show that second-order robustness is equivalent to the boundedness of both the estimator's estimating function and its derivative with respect to the parameter. It implies, at the same time, (i) variance-robustness and (ii) robustness of higher-order saddlepoint approximations to the estimator's finite sam- ple density. The proposed construction of second-order robust M-estimators is fairly general and potentially useful in a variety of relevant settings. Besides the theoretical contributions, we discuss the main computational issues and provide an algorithm for the implementation of second-order robust M-estimators. Finally, we illustrate our theory by Monte Carlo simulation and in a real-data estimation of the maximal losses of Nikkei 225 index returns. Our findings indicate that second-order robust estimators can improve on other widely-applied robust esti- mators, in terms of efficiency and robustness, for moderate to small sample sizes and in the presence of deviations from ideal parametric models.
Language
English
Keywords
Von Mises Expansion
M -estimator
Robustness
Saddlepoint
Generalized extreme value distribution.
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
Taylor & Francis Group
Publisher place
Philadelphia, Pa.
Volume
107
Number
500
Start page
1546
End page
1557
Pages
12
URL
https://www.alexandria.unisg.ch/handle/20.500.14171/90552
Subject(s)

economics

Division(s)

s/bf - Swiss Institut...

Eprints ID
229741

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