Exponential Tilting for Zero-inflated Interval Regression with Applications to Cyber Security Survey Data

Cristian Roner (), Claudia Di Caterina () and Davide Ferrari ()
Additional contact information
Cristian Roner: Free University of Bozen-Bolzano, Italy
Claudia Di Caterina: Free University of Bozen-Bolzano, Italy
Davide Ferrari: Free University of Bozen-Bolzano, Italy

No BEMPS85, BEMPS - Bozen Economics & Management Paper Series from Faculty of Economics and Management at the Free University of Bozen

Abstract: Non-negative ordered survey data often exhibit an unusually high frequency of zeros in the first interval. Zero-inflated ordered probit models handle the excess of zeros by combining a split probit model and an ordered probit model. In the presence of data violating distributional assumptions, standard inference based on the maximum likelihood method gives biased estimates with large standard errors. In this paper, we consider robust inference for the zero-inflated ordered probit model based on the exponential tilting methodology. Exponential tilting selects unequal weights for the observations in such a way as to maximise the likelihood function subject to moving a given distance from equally weighted scores. As a result, observations that are incompatible with the assumed zero-inflated distribution receive a relatively small weight. Our methodology is motivated by the analysis of survey data on cyber security breaches to study the relationship between investments in cyber defences and costs from cyber breaches. Robust estimates obtained via tilting clearly show an e ect of the investments in reducing the amount of the loss from a cyber breach.

Keywords: Zero-inflation; Exponential tilting; Interval regression; Cyber security; Survey data. (search for similar items in EconPapers)
JEL-codes: C1 C13 C83 D24 D25 (search for similar items in EconPapers)
Pages: [18 pages]
Date: 2021-06
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://repec.unibz.it/bemps85.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bzn:wpaper:bemps85

Access Statistics for this paper

More papers in BEMPS - Bozen Economics & Management Paper Series from Faculty of Economics and Management at the Free University of Bozen Contact information at EDIRC.
Bibliographic data for series maintained by F. Marta L. Di Lascio () and Alessandro Fedele ().