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 probabilistic distributions of Y|X, Z|X and X, where X, Y, Z are categorical (possibly multi-dimensional) random variables. Here, we restrict to the case of no logical relations among random variables X, Y, Z. The non-uniqueness of the conditional distribution of (Y, Z)|X suggests to deal with sets of probabilities. For that we consider different strategies to get a conditional belief function for (Y, Z)|X that approximates the initial assessment in a reasonable way. In turn, such conditional belief function, together with the marginal probability distribution of X, gives rise to a joint belief function for the distribution of \(V = (X,Y,Z)\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Coletti, G., Petturiti, D., Vantaggi, B.: Conditional belief functions as lower envelopes of conditional probabilities in a finite setting. Inf. Sci. 339, 64–84 (2016)
Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting, Trends in Logic, vol. 15. Kluwer Academic Publisher, Dordrecht/Boston/London (2002)
de Cooman, G., Zaffalon, M.: Updating beliefs with incomplete observations. Artif. Intell. 159, 75–125 (2004)
Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38(2), 325–339 (1967)
Denœux, T.: Constructing belief functions from sample data using multinomial confidence regions. Int. J. Approximate Reasoning 42(3), 228–252 (2006)
Di Zio, M., Vantaggi, B.: Partial identification in statistical matching with misclassification. Int. J. Approximate Reasoning 82, 227–241 (2017)
D’Orazio, M., Di Zio, M., Scanu, M.: Statistical Matching: Theory and Practice. Wiley (2006)
Dubins, L.: Finitely additive conditional probabilities, conglomerability and disintegrations. Ann. Probab. 3(1), 89–99 (1975)
Endres, E., Fink, P., Augustin, T.: Imprecise imputation: a nonparametric micro approach reflecting the natural uncertainty of statistical matching with categorical data. J. Official Stat. 35(3), 599–624 (2019)
Grabisch, M.: Set Functions, Games and Capacities in Decision Making. Theory and Decision Library C. Springer International Publishing (2016)
Huber, P.J.: Robust Statistics. Wiley, New York (1981)
Kadane, J.B.: Some statistical problems in merging data files. J. Official Stat. 17, 423–433 (2001)
Kamakura, W.A., Wedel, M.: Statistical data fusion for cross-tabulation. J. Mark. Res. 34, 485–498 (1997)
Levi, I.: The Enterprise of Knowledge. MIT Press, Cambridge (1980)
Manski, C.: Identification Problems in the Social Sciences. Harvard University Press, Cambridge (1995)
Miranda, E., Montes, I., Vicig, P.: On the selection of an optimal outer approximation of a coherent lower probability. Fuzzy Sets and Systems (2021)
Montes, I., Miranda, E., Vicig, P.: 2-monotone outer approximations of coherent lower probabilities. Int. J. Approximate Reasoning 101, 181–205 (2018)
Montes, I., Miranda, E., Vicig, P.: Outer approximating coherent lower probabilities with belief functions. Int. J. Approximate Reasoning 110, 1–30 (2019)
Okner, B.: Constructing a new microdata base from existing microdata sets: The 1966 merge file. Ann. Econ. Soc. Meas. 1, 325–362 (1972)
Okner, B.: Data matching and merging: an overview. Ann. Econ. Soc. Meas. 3, 347–352 (1974)
Paass, G.: Statistical match: evaluation of existing procedures and improvements by using additional information. In: Orcutt, G., Quinke, H. (eds.) Microanalytic Simulation Models to Support Social and Financial Policy, vol. 1, pp. 401–422. Elsevier Science (1986)
Rubin, D.: Statistical matching using file concatenation with adjusted weights and multiple imputations. J. Bus. Econ. Stat. 2, 87–94 (1986)
Rüschendorf, L.: Fréchet-Bounds and Their Applications, Mathematics and Its Applications, vol. 67, pp. 151–187. Springer, Netherlands (1991)
Schafer, J.: Analysis of incomplete multivariate data. Chapman & Hall (1997)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Szivós, P., Rudas, T., Tóth, I.: A tax-benefit microsimulation model for hungary. In: Workshop on Microsimulation in the New Millennium: Challenges and Innovations (1998)
Vantaggi, B.: Statistical matching of multiple sources: a look through coherence. Int. J. Approximate Reasoning 49, 701–711 (2008)
Walley, P.: Coherent lower (and upper) probabilities. Department of Statistics, University of Warwick, Technical report (1981)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Williams, P.M.: Note on conditional previsions (1975), unpublished report of School of Mathematical and Physical Science, University of Sussex (Published in International Journal of Approximate Reasoning, 44, 366–383 (2007))
Wolfson, M., Gribble, S., Bordt, M., Murphy, B., Rowe, G.: The social policy simulation database and model: an example of survey and administrative data integration. Surv. Curr. Bus. 69, 36–41 (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Petturiti, D., Vantaggi, B. (2021). Dempster-Shafer Approximations and Probabilistic Bounds in Statistical Matching. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-030-86772-0_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-86771-3
Online ISBN: 978-3-030-86772-0
eBook Packages: Computer ScienceComputer Science (R0)