Two robust tools for inference about causal effects with invalid instruments

@article{Kang2020TwoRT,
  title={Two robust tools for inference about causal effects with invalid instruments},
  author={Hyunseung Kang and Youjin Lee and Tianwen Tony Cai and Dylan S. Small},
  journal={Biometrics},
  year={2020},
  volume={78},
  pages={24 - 34}
}
Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This… 
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