Statistical Papers

, Volume 60, Issue 2, pp 179–194 | Cite as

Distribution of the multivariate nonlinear LS estimator under an uncertain input

  • Andrej PázmanEmail author
Regular Article


The aim of the paper is to develop further the approach presented in Pázman (Nonlinear Stat Model, Kluwer, Dordrecht, 1993a) for the computation of the probability density of a least squares estimator for moderate size samples in nonlinear regression. We consider here cases when the variance matrix of observations is not known, hence, it can not be used for the definition of the parameter estimator. We derived ”almost exact” results, with a modified and better defined meaning of this concept. Possible applications on three variants of an experiment of heat transfer are indicated.


Nonlinear regression Curvature Projectors Probability density Properties of least squares 

Mathematics Subject Classification

62J02 Secondary 62F10 



The author thanks prof. Daniela Jarušková for helpful discussions and to the Slovak VEGA Grant No. 1/0341/19 for financial support.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovak Republic

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