Least-Squares Fitting by Monotonic Functions Having Integer Values
作者:
A.J. Goldstein,
J.B. Kruskal,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1976)
卷期:
Volume 71,
issue 354
页码: 370-373
ISSN:0162-1459
年代: 1976
DOI:10.1080/01621459.1976.10480351
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Least-squares monotone regression (also known as least-squares isotone regression) is being used increasingly. Recently, an application arose in which the fitted values are restricted to be integers. We prove that a very simple procedure yields the optimum monotonic fit subject to this restriction, or to the more general restriction that the fitted values lie in some specified closed set. This procedure is to perform unrestricted monotone regression, and then to round off each resulting value to the nearest element of the closed set. When there are two nearest elements in the closed set, either one may be chosen, subject to the preservation of monotonicity and to one minor complication.
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