Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy

Astronomy and Astrophysics – Astronomy

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Statistical Analysis, X Ray Astronomy, X Ray Binaries, Dwarf Stars, Maximum Likelihood Estimates, Regression Analysis, Stellar Luminosity, Stellar Rotation

Scientific paper

Statistical techniques suitable for the analysis of censored data, i.e., data containing both flux measurements and upper limits, are adapted to astronomical usage from the field of survival analysis, and are used in a statistical analysis of X-ray luminosities for single stars and binaries. The conditions of applicability of these methods are discussed and verified, and it is shown that neglect of the information contained in the upper limits can lead to incorrect conclusions. Several methods suitable for linear regression in the presence of censored data are discussed. A new method, based on maximum likelihood estimation in two dimensions, is developed, and is used to determine linear regression curves in the presence of arbitrarily censored data.

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