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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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