Biases from Non-Simultaneous Regression with Correlated Covariates: A Case Study from Supernova Cosmology

Abstract

Several Type Ia supernova analyses make use of non-simultaneous regressions between observed supernova and host galaxy properties and supernova luminosity: first the supernova magnitudes are corrected for their light curve shape and color, and then they are separately corrected for their host galaxy masses. This two-step regression methodology does not introduce any biases when there are no correlations between the variables regressed in each correction step. However, correlations between these covariates will bias estimates of the size of the corrections, as well as estimates of the variance of the final residuals. In this work, we analyze the general case of non-simultaneous regression with correlated covariates to derive the functional forms of these biases. We also simulate this effect on data from the literature to provide corrections to remove these biases from the data sets studied. The biases examined here can be entirely avoided by using simultaneous regression techniques.

arXiv comment11 pages, 3 tables, accepted for publication in PASP

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