Gauss–Markov theorem

The set of Gauss-Markov is a mathematical theorem in the field of statistics. It is named after the mathematicians Carl Friedrich Gauss and Andrei Markov.

In words, this sentence reads: The least-squares estimator is a minimally -variant linear unbiased estimator in a linear model when the random error ( non- declared deviations):

• Are uncorrelated ( no autocorrelation ),
• Have an expected value of zero and
• The same variance have ( homoscedasticity ).

Mathematically this can be represented in the following way: Prerequisite is that you can a linear model in the form

Has available, where and are respectively -dimensional random variables are (see regression analysis). This one takes of the data matrix that has full (column) rank, ie it is or. The expected value of the error, it is believed that. Furthermore, one expects the variance of the error that applies.

Thus we obtain:

The residual sum of squares (English Residual Sum of Squares ) refers.