Skip Navigation

Biometrika 1967 54(1-2):133-145; doi:10.1093/biomet/54.1-2.133
© 1967 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by LIEBERMAN, G. J.
Right arrow Articles by HAMILTON, M. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Unlimited simultaneous discrimination intervals in regression

G. J. LIEBERMAN, R. G. MILLER, JR. and M. A. HAMILTON

Stanford University

The discrimination problem can be described as follows: The statistician has n pairs of values (x1, Y1), (x2, Y2),..., (xn, Yn) from which he estimates the regression line {alpha}+ßx. He now observes K additional observations Y1*, Y2*,..., YK* for which the corresponding independent variable values x1*, x2*,..., xK* are unknown. The statistician wishes to estimate these values of x and bracket them by means of simultaneous confidence intervals. This problem was first treated by Mandel (1968) and another solution was given by Miller (1966). When K is unknown and pomibly arbitrarily large, these results do not apply. A solution to this problem of arbitrary K is given in term of unlimited simultaneous discriminatdon intervals. Unlimited simultaneous discrimination intervals [DY– (P), DY+.(P)] are presented which are based upon the same estimated linear regression and which have the property that at least l00P per cent of the discrimination intervals will contain the true x's with confidence 1 –{alpha}. In this paper two techniques for obtaining unlimited simultaneous discrimination intervals are given. The first method is a procedure obtained through the Bonferroni inequality, while the second technique is based upon an idea of Lieberman & Miller (1963). A numerical example is analyzed. A general discussion and comparison of the two methods for finding unlimited simultaneons discrimination intervals is given.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.