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Title:
Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy
Authors:
Schmitt, J. H. M. M.
Affiliation:
AA(Harvard-Smithsonian Center for Astrophysics, Cambridge, MA)
Publication:
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 293, June 1, 1985, p. 178-191. (ApJ Homepage)
Publication Date:
06/1985
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
Statistical Analysis, X Ray Astronomy, X Ray Binaries, Dwarf Stars, Maximum Likelihood Estimates, Regression Analysis, Stellar Luminosity, Stellar Rotation
DOI:
10.1086/163224
Bibliographic Code:
1985ApJ...293..178S

Abstract

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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