Bias of LS estimators in nonlinear regression models with constraints. Part I: General case

Pázman, Andrej, and Denis, Jean-Baptiste. "Bias of LS estimators in nonlinear regression models with constraints. Part I: General case." Applications of Mathematics 44.5 (1999): 359-374. <http://eudml.org/doc/32523>.

@article{Pázman1999,
abstract = {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.},
author = {Pázman, Andrej, Denis, Jean-Baptiste},
journal = {Applications of Mathematics},
keywords = {nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints; transformation of parameters; nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints},
language = {eng},
number = {5},
pages = {359-374},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bias of LS estimators in nonlinear regression models with constraints. Part I: General case},
url = {http://eudml.org/doc/32523},
volume = {44},
year = {1999},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 5
SP - 359
EP - 374
AB - 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.
LA - eng
KW - nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints; transformation of parameters; nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints
UR - http://eudml.org/doc/32523
ER -