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Isotonic regression and its generalizations

IsoFuns.jl provides basic functions for solving isotonic regression problems:

  • (standard) isotonic regression problem
  • generalized isotonic regression problem
  • nearly isotonic regression problem
  • generalized nearly isotonic regression problem

Installation

Run Julia, enter ] to bring up Julia's package manager, and add the IsoFuns.jl package:

julia> ]
(v1.9) pkg> add https://github.com/yutomiyatake/IsoFuns.jl

Simple examples

using IsoFuns

n = 10
x = (1:n)/n + randn(n)
y = iso(x)

References

  • R. E. Barlow, D. J. Bartholomew, J. M. Bremner and H. D. Brunk: Statistical Inference Under Order Restrictions (1972)
  • P. Groeneboom and G. Jongbloed: Nonparametric Estimation Under Shape Constraints (2014)
  • T. Matsuda and Y. Miyatake: Generalized nearly isotonic regression (2022)
  • T. Robertson, F. T. Wright and R. L. Dykstra: Order Restricted Statistical Inference (1988)
  • R. J. Tibshirani, H. Hoefling and R. Tibshirani: Nearly-isotonic regression (2011)
  • C. van Eeden: Restricted Parameter Space Estimation Problems (2006)