Bias of LS estimators in nonlinear regression models with constraints. II: Biadditive models.
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.
scientific article; zbMATH DE number 2165528