Bias of LS estimators in nonlinear regression models with constraints. II: Biadditive models.
type: Item
instance of: scholarly article
title: Bias of LS estimators in nonlinear regression models with constraints. II: Biadditive models.
zbMATH Open document ID: 1060.62527
DOI: 10.1023/A:1023045028073
author: Jean-Baptiste Denis
author: Andrej Pázman
published in: Applications of Mathematics
publication date: 2005-05-04T00:00:00Z
full work available at URL: https://eudml.org/doc/32524
review text: General results given in the first part of this paper, ibid., 359--374 (1999; Zbl 1059.62557), are applied to bilinear models in ANOVA framework, called biadditive models. The determination of the approximate bias of the model parameters estimators is based on several complicated matrix expressions which are given by Jacobians and Hessians of the mean value of the observation vector and the constraints. Despite the necessity to use these complicated expressions in algorithms for the determination of the bias, the resulting formulae are surprisingly simple. In particular, the response estimators are shown to be approximately unbiased. Authors checked the validity of the approximation by simulation with a good agreement.
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62F30
zbMATH DE Number: 2165528
zbMATH Keywords: asymptotic variance
zbMATH Keywords: bilinear model
zbMATH Keywords: nonlinear least squares
zbMATH Keywords: response function
zbMATH Keywords: second order approximation
MaRDI profile type: Publication
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OpenAlex ID: W1602049210
description: scientific article; zbMATH DE number 2165528