Title: | Bias of LS estimators in nonlinear regression models with constraints. Part I: General case (English) |

Author: | Pázman, Andrej |

Author: | Denis, Jean-Baptiste |

Language: | English |

Journal: | Applications of Mathematics |

ISSN: | 0862-7940 |

Volume: | 44 |

Issue: | 5 |

Year: | 1999 |

Pages: | 359-374 |

Summary lang: | English |

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Category: | math |

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Summary: | We derive expressions for the asymptotic approximation of the bias of the least squares estimators in nonlinear regression models with parameters which are subject to nonlinear equality constraints. The approach suggested modifies the normal equations of the estimator, and approximates them up to $o_{p}( N^{-1}) $, where $N$ is the number of observations. The “bias equations” so obtained are solved under different assumptions on constraints and on the model. For functions of the parameters the invariance of the approximate bias with respect to reparametrisations is demonstrated. Singular models are considered as well, in which case the constraints may serve either to identify the parameters, or eventually to restrict the parameter space. (English) |

Keyword: | nonlinear least squares |

Keyword: | maximum likelihood |

Keyword: | asymptotic bias |

Keyword: | nonlinear constraints |

Keyword: | transformation of parameters |

MSC: | 62F12 |

MSC: | 62F30 |

MSC: | 62J02 |

idZBL: | Zbl 1059.62557 |

idMR: | MR1709501 |

DOI: | 10.1023/A:1023092911235 |

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Date available: | 2009-09-22T18:01:18Z |

Last updated: | 2015-05-20 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/133891 |

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Related article: | http://dml.cz/handle/10338.dmlcz/133892 |

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Reference: | [3] H. Cramér: Mathematical Methods of Statistics, 13th edition.Princeton University Press, Princeton, 1974. MR 1816288 |

Reference: | [4] J.-B. Denis and A. Pázman: Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models.Appl. Math. 44 (1999), 375–403. MR 1709502, 10.1023/A:1023045028073 |

Reference: | [5] A. Pázman: Nonlinear statistical models.Kluwer Academic Publishers, Dordrecht, 1993. MR 1254661 |

Reference: | [6] A. Pázman: Bias of the MLE in singular nonlinear regression models.(to appear). MR 0483216 |

Reference: | [7] A. Pázman and J.-B. Denis: Bias in nonlinear regression models with constrained parameters.Technical report n$^{\circ }$ 4, Unité de biométrie INRA, Versailles, 1997. |

Reference: | [8] S.D. Silvey: The Lagrangian multiplier test. Annals of Mathematical Statistics.30 (1959), 389–407. MR 0104307, 10.1214/aoms/1177706259 |

Reference: | [9] S.D. Silvey: Statistical Inference, 3rd edition.Chapman and Hall, London, 1979. MR 0500810 |

Reference: | [10] C.R. Rao and S.K. Mitra: Generalized inverse of matrices and its applications.John Wiley, New York, 1971. MR 0338013 |

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