Joint work with Erricos Kontoghiorghes, University of Cyprus and Queen Mary, University of London.

The problem of deleting observations (downdating) from the general linear (GLM) and the Seemingly Unrelated Regressions (SUR) model is considered. It is shown that the downdating problem is equivalent in updating the GLM (or the SUR model) with the imaginary deleted observations. This results in a model with undefinite dispersion matrix and comprising complex covariance values. Its solution is obtained by treating the problem as a generalised linear least squares problem (GLLSP) and obtains the solution by using the QR decomposition. Although hyperbolic reflections are used, computations do not involve complex arithmetic. The computational complexity of the proposed strategy does not depend on the remaining number of observations in the model, but on the number of the deleted observations and variables. A block strategy exploiting the non-dense triangular structure of the matrices is developed. Efficient algorithms for the re-estimation of the SUR model after deleting observations are also presented.