Distribution of the multivariate nonlinear LS estimator under an uncertain input
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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.
KeywordsNonlinear regression Curvature Projectors Probability density Properties of least squares
Mathematics Subject Classification62J02 Secondary 62F10
The author thanks prof. Daniela Jarušková for helpful discussions and to the Slovak VEGA Grant No. 1/0341/19 for financial support.