Based on observations from the Hipparcos astrometric satellite operated by the European Space Agency (ESA 1997).

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ESA-PRODEX contract 13318/98/NL/VJ.

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...

Scientific Collaborator, F.N.R.S., Belgium.

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... A. Jorissen

Research Associate, F.N.R.S., Belgium.

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... number

In order to have a unique expression for $\chi ^2$ regardless of the dataset available (FAST, NDAC or both), we always write V_j as a 2 by 2 matrix. When, for whatever reason, a measurement from only one consortium is used, that observation is duplicated and its weight divided by two ( $V_j=\mbox{diag}(2\sigma_j^2,2\sigma_j^2)$ ). There is no change on the actual value of $\chi ^2$ but its expression is easier (though not faster!) to evaluate.

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... one

We are indebted to A. Albert for suggesting this trick.

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... estimators

$\chi ^2$ is a maximum-likelihood estimator provided that the measurement errors are normally distributed.

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