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Statistical methods for astronomical data with upper limits. II - Correlation and regression
Isobe, T.; Feigelson, E. D.; Nelson, P. I.
AA(Pennsylvania State University, University Park), AB(Pennsylvania State University, University Park), AC(Kansas State University of Agriculture and Applied Science, Manhattan)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 306, July 15, 1986, p. 490-507. (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Astronomy, Bivariate Analysis, Censored Data (Mathematics), Data Correlation, Data Reduction, Regression Analysis, Distribution Functions, Estimating, Infrared Astronomy Satellite, Monte Carlo Method, Radio Galaxies, Rank Tests, Seyfert Galaxies, Significance, Statistical Tests, X Ray Astronomy
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Statistical methods for calculating correlations and regressions in bivariate censored data where the dependent variable can have upper or lower limits are presented. Cox's regression and the generalization of Kendall's rank correlation coefficient provide significant levels of correlations, and the EM algorithm, under the assumption of normally distributed errors, and its nonparametric analog using the Kaplan-Meier estimator, give estimates for the slope of a regression line. Monte Carlo simulations demonstrate that survival analysis is reliable in determining correlations between luminosities at different bands. Survival analysis is applied to CO emission in infrared galaxies, X-ray emission in radio galaxies, H-alpha emission in cooling cluster cores, and radio emission in Seyfert galaxies.

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