Algorithms and error estimations for monotone regression on partially preordered sets
Monotone (or isotonic) regression plays an important role in data analysis and in other fields. In many cases the monotonicity is only defined for a partial instead of a total preorder. No efficient algorithm is known which solves the general problem in a finite number of steps. For an approximate solution of the optimum some error estimations are given. Moreover, some new results concerning monotone regression and the treatment of missing values are presented in this paper.
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Volume (Year): 98 (2007)
Issue (Month): 5 (May)
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References listed on IDEAS
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- Jan Leeuw, 1977. "Correctness of Kruskal's algorithms for monotone regression with ties," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 141-144, March.
- Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
- J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
- Forrest Young & Yoshio Takane & Jan Leeuw, 1978. "The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 279-281, June.
- J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
- Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 357-388, December.
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