Pázman, Andrej; Denis, Jean-Baptiste Bias of LS estimators in nonlinear regression models with constraints. I: General case. (English) Zbl 1059.62557 Appl. Math., Praha 44, No. 5, 359-374 (1999). An asymptotic approximation of the bias of least squares estimators in nonlinear regression models with parameters which are subject to nonlinear equality constraints is derived. The normality of the observation vector is assumed, however under some conditions the results are valid for non-normal distribution as well. Different assumptions on constraints and on the model are taken into account. For functions of the parameters the invariance of the approximate bias with respect to reparametrization is demonstrated. Singular models are considered as well. Reviewer: Lubomír Kubáček (Olomouc) Cited in 1 ReviewCited in 5 Documents MSC: 62J02 General nonlinear regression 62F12 Asymptotic properties of parametric estimators 62F30 Parametric inference under constraints Keywords:nonlinear least squares; maximum likelihood; asymptotic bias; nonlinear constraints Citations:Zbl 1060.62527 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] M.J. Box: Bias in nonlinear estimation. Journal of the Royal Statistical Society B 33 (1971), 171-201. · Zbl 0232.62029 [2] D.R. Cox and E.J. Snell: A general definition of residuals. Journal of the Royal Statistical Society B 30 (1968), 248-275. · Zbl 0164.48903 [3] H. Cramér: Mathematical Methods of Statistics, 13th edition. Princeton University Press, Princeton, 1974. [4] J.-B. Denis and A. Pázman: Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models. Appl. Math. 44 (1999), 375-403. · Zbl 1060.62527 · doi:10.1023/A:1023045028073 [5] A. Pázman: Nonlinear statistical models. Kluwer Academic Publishers, Dordrecht, 1993. · Zbl 0808.62058 [6] A. Pázman: Bias of the MLE in singular nonlinear regression models. [7] A. Pázman and J.-B. Denis: Bias in nonlinear regression models with constrained parameters. Technical report n\(^{\circ }\) 4, Unité de biométrie INRA, Versailles, 1997. [8] S.D. Silvey: The Lagrangian multiplier test. Annals of Mathematical Statistics. 30 (1959), 389-407. · Zbl 0090.36302 · doi:10.1214/aoms/1177706259 [9] S.D. Silvey: Statistical Inference, 3rd edition. Chapman and Hall, London, 1979. [10] C.R. Rao and S.K. Mitra: Generalized inverse of matrices and its applications. John Wiley, New York, 1971. · Zbl 0236.15004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.