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Distribution of the multivariate nonlinear LS estimator under an uncertain input

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  • Andrej Pázman

    (Comenius University)

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.

Suggested Citation

  • Andrej Pázman, 2019. "Distribution of the multivariate nonlinear LS estimator under an uncertain input," Statistical Papers, Springer, vol. 60(2), pages 529-544, April.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:2:d:10.1007_s00362-018-01081-9
    DOI: 10.1007/s00362-018-01081-9
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    References listed on IDEAS

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    1. Eugene Demidenko, 2017. "Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 636-665, September.
    2. Hougaard, Philip, 1985. "Saddlepoint approximations for curved exponential families," Statistics & Probability Letters, Elsevier, vol. 3(3), pages 161-166, June.
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