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
Enlaces
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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.