A Cantelli-Type Inequality for Constructing Non-Parametric P-Boxes Based on Exchangeability

Matthias Troffaes, Tathagata Basu
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:386-393, 2019.

Abstract

In this paper we prove a new probability inequality that can be used to construct p-boxes in a non-parametric fashion, using the sample mean and sample standard deviation instead of the true mean and true standard deviation. The inequality relies only on exchangeability and boundedness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-troffaes19a, title = {A Cantelli-Type Inequality for Constructing Non-Parametric P-Boxes Based on Exchangeability}, author = {Troffaes, Matthias and Basu, Tathagata}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {386--393}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/troffaes19a/troffaes19a.pdf}, url = {https://proceedings.mlr.press/v103/troffaes19a.html}, abstract = {In this paper we prove a new probability inequality that can be used to construct p-boxes in a non-parametric fashion, using the sample mean and sample standard deviation instead of the true mean and true standard deviation. The inequality relies only on exchangeability and boundedness.} }
Endnote
%0 Conference Paper %T A Cantelli-Type Inequality for Constructing Non-Parametric P-Boxes Based on Exchangeability %A Matthias Troffaes %A Tathagata Basu %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-troffaes19a %I PMLR %P 386--393 %U https://proceedings.mlr.press/v103/troffaes19a.html %V 103 %X In this paper we prove a new probability inequality that can be used to construct p-boxes in a non-parametric fashion, using the sample mean and sample standard deviation instead of the true mean and true standard deviation. The inequality relies only on exchangeability and boundedness.
APA
Troffaes, M. & Basu, T.. (2019). A Cantelli-Type Inequality for Constructing Non-Parametric P-Boxes Based on Exchangeability. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:386-393 Available from https://proceedings.mlr.press/v103/troffaes19a.html.

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