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  "Title": "Compute Least Squares Estimates of One Bounded or Two Ordered\nIsotonic Regression Curves",
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  "Date": "2026-04-26",
  "Authors@R": "c(person(given = \"Fadoua\", family = \"Balabdaoui\", role = \"aut\", email = \"fadoua.balabdaoui@stat.math.ethz.ch\"),\nperson(given = \"Kaspar\", family = \"Rufibach\", role = c(\"aut\", \"cre\"), email = \"kaspar.rufibach@gmail.com\"),\nperson(given = \"Filippo\", family = \"Santambrogio\", role = \"aut\", email = \"santambrogio@math.univ-lyon1.fr\"))",
  "Description": "We consider the problem of estimating two isotonic\nregression curves g1* and g2* under the constraint that they\nare ordered, i.e. g1* <= g2*. Given two sets of n data points\ny_1, ..., y_n and z_1, ..., z_n that are observed at (the same)\ndeterministic design points x_1, ..., x_n, the estimates are\nobtained by minimizing the Least Squares criterion L(a, b) =\nsum_{i=1}^n (y_i - a_i)^2 w1(x_i) + sum_{i=1}^n (z_i - b_i)^2\nw2(x_i) over the class of pairs of vectors (a, b) such that a\nand b are isotonic and a_i <= b_i for all i = 1, ..., n. We\noffer two different approaches to compute the estimates: a\nprojected subgradient algorithm where the projection is\ncalculated using a PAVA as well as Dykstra's cyclical\nprojection algorithm.",
  "License": "GPL (>= 2)",
  "URL": "https://people.math.ethz.ch/~fadouab/,\nhttp://www.kasparrufibach.ch,\nhttps://math.univ-lyon1.fr/~santambrogio/",
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  "Author": "Fadoua Balabdaoui [aut], Kaspar Rufibach [aut, cre], Filippo\nSantambrogio [aut]",
  "Maintainer": "Kaspar Rufibach <kaspar.rufibach@gmail.com>",
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      "page": "ordMonReg-package",
      "title": "Compute Least Squares Estimates of One Bounded or Two Ordered Isotonic Regression Curves",
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        "OrdMonReg-package",
        "OrdMonReg"
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    },
    {
      "page": "bstar_n",
      "title": "Computes explicitly known values of the estimates in the two ordered functions antitonic regression problem",
      "topics": [
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        "bstar_n"
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    },
    {
      "page": "BoundedIsoMean",
      "title": "Compute least square estimate of an iso- or antitonic function, bounded below and above by fixed functions",
      "topics": [
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        "BoundedIsoMean"
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    },
    {
      "page": "BoundedAntiMeanTwo",
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      "topics": [
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        "BoundedIsoMeanTwo"
      ]
    },
    {
      "page": "BoundedIsoMeanTwoDykstra",
      "title": "Compute solution to the problem of two ordered isotonic or antitonic curves",
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      "topics": [
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        "minK3"
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