Last but not least, Eq. (36) showed us the
equivalence between fitting data for which the leakage
matrix is not the identity, and fitting data for which it explicitly is.
This last statement is true provided that we know perfectly
well the leakage matrix. In this case the p-mode parameters fitted using MLE
are not, or very weakly, biased, and have minimum variance. For instance, we showed for the splitting that other commonly fitting methods result either in a bias and/or larger formal errors. We have also studied the effect of an
imperfect knowledge of the leakage matrix on the fitted parameters,
in order to derive the effect of systematic errors on the most
interesting parameters: the splitting and mode frequency. We found
that the central frequency is insensitive to systematic errors in the
leakage matrix, while the splitting coefficients (*a*_{i}) have a
quadratic dependence upon those errors. These systematic errors will
have influence on the inverted solar rotation profiles.

Finally, we would like to stress again that the correct statistical treatment of the p-mode data is of vital importance for deducing unbiased p-mode parameters.

Many thanks to Takashi Sekii for constructive comments on the manuscript, and for extensive cyberspace chatting :-). We are grateful to the referees for their constructive comments.

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