Geodesic
Bias of LS estimators in nonlinear regression models with constraints. Part I: General case
Applications of Mathematics, Tome 44 (1999) no. 5, pp. 359-374.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1023/A:1023092911235
Classification : 62F12, 62F30, 62J02
Keywords: nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints; transformation of parameters 
@article{10_1023_A_1023092911235,
     author = {P\'azman, Andrej and Denis, Jean-Baptiste},
     title = {Bias of {LS} estimators in nonlinear regression models with constraints. {Part} {I:} {General} case},
     journal = {Applications of Mathematics},
     pages = {359--374},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {1999},
     doi = {10.1023/A:1023092911235},
     mrnumber = {1709501},
     zbl = {1059.62557},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1023092911235/}
}
TY  - JOUR
AU  - Pázman, Andrej
AU  - Denis, Jean-Baptiste
TI  - Bias of LS estimators in nonlinear regression models with constraints. Part I: General case
JO  - Applications of Mathematics
PY  - 1999
SP  - 359
EP  - 374
VL  - 44
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1023092911235/
DO  - 10.1023/A:1023092911235
LA  - en
ID  - 10_1023_A_1023092911235
ER  - 
%0 Journal Article
%A Pázman, Andrej
%A Denis, Jean-Baptiste
%T Bias of LS estimators in nonlinear regression models with constraints. Part I: General case
%J Applications of Mathematics
%D 1999
%P 359-374
%V 44
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1023092911235/
%R 10.1023/A:1023092911235
%G en
%F 10_1023_A_1023092911235
Pázman, Andrej; Denis, Jean-Baptiste. Bias of LS estimators in nonlinear regression models with constraints. Part I: General case. Applications of Mathematics, Tome 44 (1999) no. 5, pp. 359-374. doi : 10.1023/A:1023092911235. http://geodesic.mathdoc.fr/articles/10.1023/A:1023092911235/

Cité par Sources :