ANALYSIS OF ZEEMAN EFFECT DATA IN RADIO ASTRONOMY

We discuss the analysis of Zeeman effect data in radio astronomy and in particular, extend previous techniques to include the case of low signal-to-noise ratios. We consider three statistical techniques for estimating the line-of-sight magnetic field: maximum likelihood, least-squares, and Wiener filters. For high signal-to-noise ratios, all three estimators are essentially unbiased. In the poor to moderate signal-to-noise ratio regime, we conclude that all three estimators are biased; the maximum likelihood technique yields results that are, in general, substantially less biased than least-squares and Wiener filters. However, it is possible to "debias" the least-squares results and obtain estimates that are as good as maximum likelihood under a restricted set of conditions.