### Abstract

An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo–SimulatedAnnealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.

Original language | English |
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Pages (from-to) | 13-26 |

Number of pages | 14 |

Journal | Computational Statistics and Data Analysis |

Volume | 138 |

Early online date | 26 Mar 2019 |

DOIs | |

Publication status | Published - 1 Oct 2019 |

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**A flexible sequential Monte Carlo algorithm for parametric constrained regression.** / Ng, Kenyon; Turlach, Berwin A.; Murray, Kevin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A flexible sequential Monte Carlo algorithm for parametric constrained regression

AU - Ng, Kenyon

AU - Turlach, Berwin A.

AU - Murray, Kevin

PY - 2019/10/1

Y1 - 2019/10/1

N2 - An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo–SimulatedAnnealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.

AB - An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo–SimulatedAnnealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.

KW - B-splines

KW - Constrained optimisation

KW - Rational functions

KW - Sequential Monte Carlo

KW - Shape constraints

KW - Simulated annealing

UR - http://www.scopus.com/inward/record.url?scp=85063904296&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2019.03.011

DO - 10.1016/j.csda.2019.03.011

M3 - Article

VL - 138

SP - 13

EP - 26

JO - Computational Statistics & Data Analysis

JF - Computational Statistics & Data Analysis

SN - 0167-9473

ER -