Many economic applications require to integrate information coming from different data sources. In this work we consider a specific integration problem, called statistical matching, referring to integration of data sets where some variables are separately observed and some others are observed in all the data sets. This problem leads to the issue of non-uniqueness for the compatible (conditional) distributions and so it suggests to deal with sets of probabilities. For that we consider different strategies to get a (conditional) belief function that approximates the lower envelope of the class of compatible (conditional) probabilities. We first analyze the case without logical constraints among the variables and then generalize the obtained results by allowing for logical constraints. We finally show an application to real data.

Probability envelopes and their Dempster-Shafer approximations in statistical matching / Petturiti, D.; Vantaggi, B.. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 150:(2022), pp. 199-222. [10.1016/j.ijar.2022.08.011]

### Probability envelopes and their Dempster-Shafer approximations in statistical matching

#### Abstract

Many economic applications require to integrate information coming from different data sources. In this work we consider a specific integration problem, called statistical matching, referring to integration of data sets where some variables are separately observed and some others are observed in all the data sets. This problem leads to the issue of non-uniqueness for the compatible (conditional) distributions and so it suggests to deal with sets of probabilities. For that we consider different strategies to get a (conditional) belief function that approximates the lower envelope of the class of compatible (conditional) probabilities. We first analyze the case without logical constraints among the variables and then generalize the obtained results by allowing for logical constraints. We finally show an application to real data.
##### Scheda breve Scheda completa
2022
Approximations; Belief functions; Inference; Lower envelopes; Statistical matching
01 Pubblicazione su rivista::01a Articolo in rivista
Probability envelopes and their Dempster-Shafer approximations in statistical matching / Petturiti, D.; Vantaggi, B.. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 150:(2022), pp. 199-222. [10.1016/j.ijar.2022.08.011]
File allegati a questo prodotto
File
Vantaggi_Probability-envelopes_2022.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Dimensione 593.59 kB

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1663523`
• ND
• 1
• 2