Abstract
Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.
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Reference note
Van Eeden, C.Testing and estimating ordered parameters of probability distributions. Unpublished doctoral dissertation, University of Amsterdam, 1958.
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Comments by Dr. J. B. Kruskal have been most helpful.
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de Leeuw, J. Correctness of Kruskal's algorithms for monotone regression with ties. Psychometrika 42, 141–144 (1977). https://doi.org/10.1007/BF02293750
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DOI: https://doi.org/10.1007/BF02293750