Weighted Mean - Accounting For Correlations

Accounting For Correlations

In the general case, suppose that, is the covariance matrix relating the quantities, is the common mean to be estimated, and is the design matrix (of length ). The Gauss–Markov theorem states that the estimate of the mean having minimum variance is given by:

and

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    I, who am king of the matter I treat, and who owe an accounting for it to no one, do not for all that believe myself in all I write. I often hazard sallies of my mind which I mistrust.
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    I, who am king of the matter I treat, and who owe an accounting for it to no one, do not for all that believe myself in all I write. I often hazard sallies of my mind which I mistrust.
    Michel de Montaigne (1533–1592)