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A universal formula of maximum likelihood estimation of variance-covariance components

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Abstract

The derivation of a universal formula for the variance-covariance component estimation is discussed. The formula is derived adopting the universal functional model (the condition adjustment with unknown parameters and constraints among the parameters),and is based on the maximum likelihood principle. The derived formula in this paper can be applied to all adjustment models for estimating variance-covariance components, which expands the formulas given by K. Kubik (1970)and K. R. Koch (1986).Besides, it is proved that the estimator given in this paper is equivalent to that of Helmert type and best quadratic unbiased estimation (BQUE).

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Authors and Affiliations

  1. Wuhan Technical University of Surveying and Mapping, 430070, Wuhan, Hubei, P.R. China

    Z. C. Yu

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  1. Z. C. Yu
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Yu, Z.C. A universal formula of maximum likelihood estimation of variance-covariance components. Journal of Geodesy 70, 233–240 (1996). https://doi.org/10.1007/BF00873704

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  • DOI: https://doi.org/10.1007/BF00873704

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