Semiparametric theory and empirical processes in causal inference

  title={Semiparametric theory and empirical processes in causal inference},
  author={Edward H. Kennedy},
  journal={arXiv: Statistics Theory},
  • Edward H. Kennedy
  • Published 15 October 2015
  • Mathematics, Economics
  • arXiv: Statistics Theory
In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the… 
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  • J. Am. Sta t. Assoc.90, 106–121
  • 1995