Abstract
In this work we present a demonstration for the multinomial version of de Finettiās Representation Theorem. We use characteristic functions, following his first demonstration for binary random quantities, but simplify the argument through forward operators.
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Notes
- 1.
- 2.
The limits with forward operators are well defined because the set of polynomial operators induces an algebra that is isomorphic to the algebra of polynomials in real or complex variables. See [4].
- 3.
It is possible to find the distribution function inverting the characteristic function.
References
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Acknowledgements
Marcio Diniz was supported by FAPESP (Sao Paulo Research Foundation), under the project 2012/14764-0, and wishes to thank SYSTeMs Research Group at Ghent University for its hospitality and support.
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Diniz, M.A., Polpo, A. (2014). A Simple Proof for the Multinomial Version of the Representation Theorem. In: Lanzarone, E., Ieva, F. (eds) The Contribution of Young Researchers to Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 63. Springer, Cham. https://doi.org/10.1007/978-3-319-02084-6_4
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