Title
Construction of a conservative confidence region from projections of an exact confidence region in multiple linear regression
Keywords
Bonferroni; Scheffe; Working-Hotelling
Abstract
The problem of constructing a confidence region for simultaneously estimating p, p ≥ 2, linear regression parameters for which confidence statements can be made on the individual parameters is revisited. Here, an intercept may be included among the p parameters. The technique is due to Working and Hotelling (1929) and Scheffe (1959) and uses the p separate projections of the exact (1 – α)100% confidence ellipsoid (ellipse if p = 2) to give confidence intervals for each regression parameter. The Cartesian product of these p confidence intervals gives a p-dimensional rectangle that contains the confidence ellipsoid and hence has a joint confidence coefficient of at least (1 – α). A simple calculus proof is given to determine these projections. The projection procedure is compared with the Bonferroni procedure for this case. © 1994 Taylor & Francis Group, LLC.
Publication Date
1-1-1994
Publication Title
American Statistician
Volume
48
Issue
2
Number of Pages
120-124
Document Type
Article
Identifier
scopus
Personal Identifier
scopus
DOI Link
https://doi.org/10.1080/00031305.1994.10476038
Copyright Status
Unknown
Socpus ID
21344483887 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/21344483887
STARS Citation
Nickerson, David M., "Construction of a conservative confidence region from projections of an exact confidence region in multiple linear regression" (1994). Scopus Export 1990s. 263.
https://stars.library.ucf.edu/scopus1990/263