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On recovering a population covariance matrix in the presence of selection bias

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  • Manabu Kuroki
  • Zhihong Cai

Abstract

This paper considers the problem of using observational data in the presence of selection bias to identify causal effects in the framework of linear structural equation models. We propose a criterion for testing whether or not observed statistical dependencies among variables are generated by conditioning on a common response variable. When the answer is affirmative, we further provide formulations for recovering the covariance matrix of the whole population from that of the selected population. The results of this paper provide guidance for reliable causal inference, based on the recovered covariance matrix obtained from the statistical information with selection bias. Copyright 2006, Oxford University Press.

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  • Manabu Kuroki & Zhihong Cai, 2006. "On recovering a population covariance matrix in the presence of selection bias," Biometrika, Biometrika Trust, vol. 93(3), pages 601-611, September.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:3:p:601-611
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    File URL: http://hdl.handle.net/10.1093/biomet/93.3.601
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    Cited by:

    1. Ryusei Shingaki & Hiroshi Kanda & Manabu Kuroki, 2021. "Selection and integration of generalized instrumental variables for estimating total effects," Statistical Papers, Springer, vol. 62(5), pages 2355-2381, October.
    2. Sanjay Chaudhuri, 2014. "Qualitative inequalities for squared partial correlations of a Gaussian random vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 345-367, April.

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