Sponsor
The research of Anirban DasGupta was partially supported by ELS-90014395 grant at Purdue University.
Published In
Sankhya-Series A-Mathematical Statistics and Probability
Document Type
Pre-Print
Publication Date
5-24-2024
Subjects
Mathematics
Abstract
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X ∼ N(µ, σ2). Here we extend this result to obtaining 1-sample confidence intervals for σ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension.
Rights
© Copyright the author(s) 2024
Locate the Document
DOI
10.1007/s13171-023-00338-2
Persistent Identifier
https://archives.pdx.edu/ds/psu/42015
Citation Details
Published as: DasGupta, A., & Portnoy, S. (2024). Valid Confidence Intervals for µ,σWhen There Is Only One Observation Available. Sankhya A.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Valid Confidence Intervals for µ,σ When There Is Only One Observation Available. Sankhya A, 1-12.