Possibility Measures for Valid Statistical Inference Based on Censored Data

Joyce Cahoon, Ryan Martin
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:49-58, 2019.

Abstract

Inferential challenges that arise when data are corrupted by censoring have been extensively studied under the classical frameworks. In this paper, we provide an alternative approach based on a generalized inferential model whose output is a data-dependent possibility distribution. This construction is driven by an association between the censored data, parameter of interest, and unobserved auxiliary variable that takes the form of a relative likelihood. The possibility distribution then emerges from the introduction of a nested random set designed to predict that unobserved auxiliary variable and is calibrated to achieve certain frequentist guarantees. The performance of the proposed method is investigated using real and simulated data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-cahoon19a, title = {Possibility Measures for Valid Statistical Inference Based on Censored Data}, author = {Cahoon, Joyce and Martin, Ryan}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {49--58}, 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/cahoon19a/cahoon19a.pdf}, url = {https://proceedings.mlr.press/v103/cahoon19a.html}, abstract = {Inferential challenges that arise when data are corrupted by censoring have been extensively studied under the classical frameworks. In this paper, we provide an alternative approach based on a generalized inferential model whose output is a data-dependent possibility distribution. This construction is driven by an association between the censored data, parameter of interest, and unobserved auxiliary variable that takes the form of a relative likelihood. The possibility distribution then emerges from the introduction of a nested random set designed to predict that unobserved auxiliary variable and is calibrated to achieve certain frequentist guarantees. The performance of the proposed method is investigated using real and simulated data.} }
Endnote
%0 Conference Paper %T Possibility Measures for Valid Statistical Inference Based on Censored Data %A Joyce Cahoon %A Ryan Martin %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-cahoon19a %I PMLR %P 49--58 %U https://proceedings.mlr.press/v103/cahoon19a.html %V 103 %X Inferential challenges that arise when data are corrupted by censoring have been extensively studied under the classical frameworks. In this paper, we provide an alternative approach based on a generalized inferential model whose output is a data-dependent possibility distribution. This construction is driven by an association between the censored data, parameter of interest, and unobserved auxiliary variable that takes the form of a relative likelihood. The possibility distribution then emerges from the introduction of a nested random set designed to predict that unobserved auxiliary variable and is calibrated to achieve certain frequentist guarantees. The performance of the proposed method is investigated using real and simulated data.
APA
Cahoon, J. & Martin, R.. (2019). Possibility Measures for Valid Statistical Inference Based on Censored Data. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:49-58 Available from https://proceedings.mlr.press/v103/cahoon19a.html.

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