Asymptotics of certain conditionally identically distributed sequences

Patrizia Berti, Emanuela Dreassi, Luca Pratelli and Pietro Rigo

Statistics & Probability Letters, 2021, vol. 168, issue C

Abstract: The probability distribution of a sequence X=(X1,X2,…) of random variables is determined by its predictive distributions P(X1∈⋅) and P(Xn+1∈⋅∣X1,…,Xn), n≥1. Motivated by applications in Bayesian predictive inference, in Berti et al. (2020), a class C of sequences is introduced by specifying such predictive distributions. Each X∈C is conditionally identically distributed. The asymptotics of X∈C is investigated in this paper. Both strong and weak limit theorems are provided. Conditions for X to converge a.s., and for X not to converge in probability, are given in terms of the predictive distributions. A stable CLT is provided as well. Such a CLT is used to obtain approximate credible intervals.

Keywords: Bayesian nonparametrics; Conditional identity in distribution; Exchangeability; Limit theorem; Predictive distribution; Predictive inference (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715220302261
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302261

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2020.108923

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().