### Abstract

The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley’s theorem is stated to extend the Modified Gauss-Newton method to this problem.

Original language | English (US) |
---|---|

Pages (from-to) | 144-147 |

Number of pages | 4 |

Journal | Journal of the American Statistical Association |

Volume | 68 |

Issue number | 341 |

DOIs | |

State | Published - Jan 1 1973 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of the American Statistical Association*,

*68*(341), 144-147. https://doi.org/10.1080/01621459.1973.10481353

}

*Journal of the American Statistical Association*, vol. 68, no. 341, pp. 144-147. https://doi.org/10.1080/01621459.1973.10481353

**Fitting segmented polynomial regression models whose join points have to be estimated.** / Gallant, Andrew Ronald; Fuller, Wayne A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fitting segmented polynomial regression models whose join points have to be estimated

AU - Gallant, Andrew Ronald

AU - Fuller, Wayne A.

PY - 1973/1/1

Y1 - 1973/1/1

N2 - The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley’s theorem is stated to extend the Modified Gauss-Newton method to this problem.

AB - The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley’s theorem is stated to extend the Modified Gauss-Newton method to this problem.

UR - http://www.scopus.com/inward/record.url?scp=84950655372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950655372&partnerID=8YFLogxK

U2 - 10.1080/01621459.1973.10481353

DO - 10.1080/01621459.1973.10481353

M3 - Article

AN - SCOPUS:84950655372

VL - 68

SP - 144

EP - 147

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 341

ER -