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The traditional Schmidt density estimator has been proven to be unbiased and effective in a magnitude-limited sample. Previously, efforts have been made to generalize it for populations with non-uniform density and proper motion-limited cases. This work shows that the then-good assumptions for a proper motion-limited sample are no longer sufficient to cope with modern data. Populations with larger differences in the kinematics as compared to the local standard of rest are most severely affected. We show that this systematic bias can be removed by treating the discovery fraction inseparable from the generalized maximum volume integrand. The treatment can be applied to any proper motion-limited sample with good knowledge of the kinematics. This work demonstrates the method through application to a mock catalogue of a white dwarf-only solar neighbourhood for various scenarios and compared against the traditional treatment using a survey with Pan-STARRS-like characteristics.
We present a new volume-limited sample of L0-T8 dwarfs out to 25 pc defined entirely by parallaxes, using our recent measurements from UKIRT/WFCAM along with Gaia DR2 and literature parallaxes. With 369 members, our sample is the largest parallax-def
We have derived the absolute proper motion (PM) of the globular cluster M55 using a large set of CCD images collected with the du Pont telescope between 1997 and 2008. We find (PM_RA*cos(DEC), PM_DEC) = (-3.31 +/- 0.10, -9.14 +/- 0.15) mas/yr relativ
We conducted a spectropolarimetic survey of 58 high proper-motion white dwarfs which achieved uncertainties of >2 kG in the Halpha line and >5 kG in the upper Balmer line series. The survey aimed at detecting low magnetic fields (< 100 kG) and helped
We present a flux-limited sample of $zsim0.3$ Ly$alpha$ emitters (LAEs) from Galaxy Evolution Explorer (GALEX) grism spectroscopic data. The published GALEX $zsim0.3$ LAE sample is pre-selected from continuum-bright objects and thus is biased against
The maximum likelihood estimator plays a fundamental role in statistics. However, for many models, the estimators do not have closed-form expressions. This limitation can be significant in situations where estimates and predictions need to be compute