= T. E. Lutz
{c}
<T. E. Lutz> and <D. H. Kelker> analyzed systematic effects in <luminosity> calibration from noisy <stellar parallax>[stellar parallaxes]. Their 1973 treatment assumes a spatial distribution of <stars> and a model for <measurement uncertainty>, then examines the inferred <absolute magnitudes>.
The resulting <Lutz-Kelker bias> illustrates why an unbiased measurement of one quantity does not automatically yield unbiased inference after selection or a nonlinear transformation. The calculation's population and measurement assumptions are essential to interpreting the proposed corrections.<On the Use of Trigonometric Parallaxes for the Calibration of Luminosity Systems: Theory by T. E. Lutz and D. H. Kelker>[pp. 573–574, Introduction and The Distribution Function: parallax errors, spatial distribution and magnitude calibration]{ref}
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