Resources for Learning Semi-parametric Theory

November 11, 2024

This post gathers resources that may be helpful in learning the semi-parametric statistical theory that is relevant to statistical methods development for causal inference. I intend to continually update this post. BibTex is provided at the bottom.

Articles

All of Edward Kennedy’s expository writing on the subject is excellent; I recommend starting with the following two articles:

For a big-picture review of Targeted Learning and Double Machine Learning:

Online Resources

Books

There are several books by van der Vaart and colleagues that serve as foundational references for semi-parametric theory. You will often see both of the following books cited in papers.

Both of the Targeted Learning books by van der Laan and Rose are the canonical texts on the subject:

Other books:

Bibtex

Note the correct capitalization: “van der Laan” and “van der Vaart”.

@misc{kennedy2023review,
      title={Semiparametric doubly robust targeted double machine learning: a review}, 
      author={Edward H. Kennedy},
      year={2023},
      eprint={2203.06469},
      archivePrefix={arXiv},
      primaryClass={stat.ME},
      url={https://arxiv.org/abs/2203.06469}, 
}

@article{fisher2021influence,
  author = {Aaron Fisher and Edward H. Kennedy},
  title = {Visually Communicating and Teaching Intuition for Influence Functions},
  journal = {The American Statistician},
  volume = {75},
  number = {2},
  pages = {162--172},
  year = {2021},
  publisher = {ASA Website},
  doi = {10.1080/00031305.2020.1717620},
  URL = {https://doi.org/10.1080/00031305.2020.1717620},
  eprint = {https://doi.org/10.1080/00031305.2020.1717620}
}

@article{diaz2019machinelearning,
    author = {Díaz, Iván},
    title = "{Machine learning in the estimation of causal effects: targeted minimum loss-based estimation and double/debiased machine learning}",
    journal = {Biostatistics},
    volume = {21},
    number = {2},
    pages = {353-358},
    year = {2019},
    month = {11},
    issn = {1465-4644},
    doi = {10.1093/biostatistics/kxz042},
    url = {https://doi.org/10.1093/biostatistics/kxz042},
    eprint = {https://academic.oup.com/biostatistics/article-pdf/21/2/353/32914770/kxz042.pdf},
}

@book{vdlrose2011targetd,
  author={Mark {van der Laan} and Sherri Rose},
  title={Targeted Learning},
  subtitle={Causal Inference for Observational and Experimental Data},
  year={2011},
  series={Springer Series in Statistics},
  publisher={Springer New York, NY},
  doi={https://doi.org/10.1007/978-1-4419-9782-1}
}

@book{vdlrose2018targetd,
  author={Mark {van der Laan} and Sherri Rose},
  title={Targeted Learning in Data Science},
  subtitle={Causal Inference for Complex Longitudinal Studies},
  year={2018},
  series={Springer Series in Statistics},
  publisher={Springer Cham},
  doi={https://doi.org/10.1007/978-3-319-65304-4}
}

@book{vdv1998asymptotics, 
  place={Cambridge},
  series={Cambridge Series in Statistical and Probabilistic Mathematics},
  title={Asymptotic Statistics},
  publisher={Cambridge University Press},
  author={Aad W. {van der Vaart}},
  year={1998}, 
  collection={Cambridge Series in Statistical and Probabilistic Mathematics}
} 

@book{vdv2023weakconvergence,
  edition={2},
  year={2023},
  series={Springer Series in Statistics},
  publisher={Springer Cham},
  author={Aad W. {van der Vaart} and Jon A. Wellner},
  title={Weak Convergence and Empirical Processes},
  subtitle={With Applications to Statistics},
  doi={10.1007/978-3-031-29040-4}
}

@book{bickel1993semiparametric,
  author={Peter J. Bickel and Chris A.J. Klaassen and Ya'acov Ritov and Jon A. Wellner},
  title={Efficient and Adaptive Estimation for Semiparametric Models},
  year={1993},
  publisher={Springer New York, NY}
}

@book{tsiatis2006theory,
  author={Anastasios A. Tsiatis},
  title={Semiparametric Theory and Missing Data},
  doi={10.1007/0-387-37345-4},
  publisher={Springer New York, NY},
  series={Springer Series in Statistics},
  year={2006}
}

@book{kosorok2008semiparametric,
  title={Introduction to Empirical Processes and Semiparametric Inference},
  author={Michael R. Kosorok},
  doi={10.1007/978-0-387-74978-5},
  series={Springer Series in Statistics},
  publisher={Springer New York, NY},
  year={2008}
}