Nonparametric predictive inference and interval probability

Augustin, T.; Coolen, F.P.A.

Abstract

The assumption A(n), proposed by Hill (J. Amer. Statist. Assoc. 63 (1968) 677), provides a natural basis for low structure non-parametric predictive inference, and has been justified in the Bayesian framework. This paper embeds A(n)-based inference into the theory of interval probability, by showing that the corresponding bounds are totally monotone F-probability and coherent. Similar attractive internal consistency results are proven to hold for conditioning and updating.

Citation

Augustin, T., & Coolen, F. (2004). Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference, 124(2), 251-272. https://doi.org/10.1016/j.jspi.2003.07.003

• Journal Article Type: Article
• Publication Date: Sep 1, 2004
• Deposit Date: Apr 26, 2007
• Journal: Journal of Statistical Planning and Inference
• Print ISSN: 0378-3758
• Electronic ISSN: 1873-1171
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 124
• Issue: 2
• Pages: 251-272
• DOI: https://doi.org/10.1016/j.jspi.2003.07.003
• Keywords: A(n), Capacities, Conditioning, Consistency, Imprecise probabilities, Interval probability, Non-parametrics, Low structure inference, Predictive inference, Updating.
• Public URL: https://durham-repository.worktribe.com/output/1567641