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Title: Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models (English)
Author: Denis, Jean-Baptiste
Author: Pázman, Andrej
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 44
Issue: 5
Year: 1999
Pages: 375-403
Summary lang: English
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Category: math
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Summary: General results giving approximate bias for nonlinear models with constrained parameters are applied to bilinear models in anova framework, called biadditive models. Known results on the information matrix and the asymptotic variance matrix of the parameters are summarized, and the Jacobians and Hessians of the response and of the constraints are derived. These intermediate results are the basis for any subsequent second order study of the model. Despite the large number of parameters involved, bias formulæ turn out to be quite simple due to the orthogonal structure of the model. In particular, the response estimators are shown to be approximately unbiased. Some simulations assess the validity of the approximations. (English)
Keyword: asymptotic variance
Keyword: bilinear model
Keyword: nonlinear least squares
Keyword: response function
Keyword: second order approximation
MSC: 62F12
MSC: 62F30
MSC: 62J02
idZBL: Zbl 1060.62527
idMR: MR1709502
DOI: 10.1023/A:1023045028073
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Date available: 2009-09-22T18:01:23Z
Last updated: 2015-05-20
Stable URL: http://hdl.handle.net/10338.dmlcz/133892
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Related article: http://dml.cz/handle/10338.dmlcz/133891
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