Distribution of the multivariate nonlinear LS estimator under an uncertain input

Andrej Pázman ()
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Andrej Pázman: Comenius University

Statistical Papers, 2019, vol. 60, issue 2, No 12, 529-544

Abstract: Abstract 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.

Keywords: Nonlinear regression; Curvature; Projectors; Probability density; Properties of least squares; 62J02; Secondary 62F10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00362-018-01081-9

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