August 2022 Modeling the Occurrence of Events Subject to a Reporting Delay via an EM Algorithm
Roel Verbelen, Katrien Antonio, Gerda Claeskens, Jonas Crevecoeur
Author Affiliations +
Statist. Sci. 37(3): 394-410 (August 2022). DOI: 10.1214/21-STS831


A delay between the occurrence and the reporting of events often has practical implications such as for the amount of capital to hold for insurance companies, or for taking preventive actions in case of infectious diseases. The accurate estimation of the number of incurred but not (yet) reported events forms an essential part of properly dealing with this phenomenon. We review the current practice for analysing such data and we present a flexible regression framework to jointly estimate the occurrence and reporting of events. By linking this setting to an incomplete data problem, estimation is performed via an expectation-maximization algorithm. The resulting method is elegant, easy to understand and implement, and provides refined insights in the nowcasts. The proposed methodology is applied to a European general liability portfolio in insurance.

Funding Statement

Support is acknowledged from the agency for Innovation by Science and Technology (IWT 131173), Research Foundation Flanders (FWO 11G4619N), the Argenta Research Chair at KU Leuven, CNP Assurances via the DIALog Excellence Chair and from KU Leuven’s research council projects COMPACT C24/15/001 and C1/16/20/002.


The authors are grateful to the Editors, Associate Editor and the referee for the valuable comments and suggestions.


Download Citation

Roel Verbelen. Katrien Antonio. Gerda Claeskens. Jonas Crevecoeur. "Modeling the Occurrence of Events Subject to a Reporting Delay via an EM Algorithm." Statist. Sci. 37 (3) 394 - 410, August 2022.


Published: August 2022
First available in Project Euclid: 21 June 2022

MathSciNet: MR4444374
zbMATH: 07569968
Digital Object Identifier: 10.1214/21-STS831

Keywords: EM algorithm , nowcasting , Poisson regression model , reporting delay

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.37 • No. 3 • August 2022
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