On the Gauss–Helmert model with a singular dispersion matrix where BQ is of smaller rank than B

• Frank Neitzel ^[1] ; Burkhard Schaffrin ^[2]
  1. [1] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 291, Nº 1 (1 January 2016), 2016, págs. 458-467
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.03.006
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• Resumen

  • The case of a singular dispersion matrix within the Gauss–Helmert Model has been considered before, usually assuming a sufficiently small rank deficiency in order to guarantee a unique solution for both the residual vector as well as the estimated parameter vector of type Best Linear Uniformly Unbiased Estimate (BLUUE). In this contribution the emphasis is shifted towards establishing necessary and sufficient conditions for a unique residual vector, along with a unique estimate of type Best Linear Uniformly Minimum Bias Estimate (BLUMBE) for the parameter vector. Should uniformly unbiased estimates exist, the BLUMBE obviously becomes the BLUUE.