Journal ArticleDOI
The Isotonic Regression Problem and its Dual
Richard E. Barlow,H. D. Brunk +1 more
TLDR
In this article, a generalization of the Fenchel dual isotonic regression problem has been proposed to solve the problem of inventory theory and statistics, and a function of the isotonic regressions has been defined to solve these problems.Abstract:
The isotonic regression problem is to minimize Σt i = 1 [gi − xi]2wi subject to xi ≤ xj when where wi>0 and gi (i= 1, 2, …, k) are given and is a specified partial ordering on {1, 2, …, k}. The solution is called the isotonic regression on g. We formulate a generalization of this problem and calculate its Fenchel dual. A function of the isotonic regression also solves these problems. Problems in inventory theory and statistics are identified as dual isotonic regression problems.read more
Citations
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Boosting the accuracy of differentially private histograms through consistency
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Book ChapterDOI
A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces
TL;DR: In this article, it is shown that if the constraint region can be expressed as a finite intersection of simpler convex regions, then one can obtain the projection onto the intersection by performing a series of projections only onto the simpler regions.
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Additive structure in qualitative data: An alternating least squares method with optimal scaling features
TL;DR: In this article, the additive structure of data that can be measured at the nominal, ordinal or cardinal levels, may be obtained from either a discrete or continuous source, and may have known degrees of imprecision.
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