Gauss-Markov theorem

The matrix IzmxN containing the model parameters can then be directly estimated using the Gauss-Markov theorem to find the least squares solution of generic linear problems written in matrix form [37] ... 

The probability density functions of the observations are generally unknown, but the Gauss-Markov theorem ensures that least-squares is always an acceptable estimator. However, the results of least squares are strongly influenced by discordant observations, so-called outliers. The robust-resistant techniques use weight-modification functions of O—Cy which progressively down-weight outliers. Tnese functions implicitly define probability functions p. They may alternatively be interpreted as an appreciation of the reliability of certain measurements. This approaches the frequently used option to simply omit discordant observations because they are judged to be unreliable. 

It should be emphasized that these results do not require an assumption of the type of the error distribution function. Moreover, it can be shown (the Gauss-Markov theorem Bard, 1974, p. 59 Hamilton, 1964, Chap. 4 Hudson, 1963, Chap. 5 Seber, 1977, Chap. 3) that... 

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