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Robust estimation in generalized linear models based on the normal quantiles of the probability integral transformation

  • Marina Valdora
  • Víctor Yohai
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Abstract

A new approach to robust estimation in generalized linear models is introduced. The idea of the method is to first transform the responses applying the composition of the normal quantile function and the probability integral transformation. Then, using that the transformed responses should follow a standard normal distribution, find the values of the parameters that minimize a robust measure of their size. In practice an approximation of this transformation is used. The proposed estimators are studied theoretically for distributions that depend on a single parameter and through simulations and examples for the particular cases of Poisson and logistic regression.

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Cite

BibTeXRIS
BibTeX
@misc{valdora2026robust,
  title = {{Robust estimation in generalized linear models based on the normal quantiles of the probability integral transformation}},
  author = {Marina Valdora and Víctor Yohai},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29385},
  eprint = {2608.29385},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29385},
}
RIS
TY  - UNPB
TI  - Robust estimation in generalized linear models based on the normal quantiles of the probability integral transformation
AU  - Marina Valdora
AU  - Víctor Yohai
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29385
UR  - https://arxiv.org/abs/2608.29385
AB  - A new approach to robust estimation in generalized linear models is introduced. The idea of the method is to first transform the responses applying the composition of the normal quantile function and the probability integral transformation. Then, using that the transformed responses should follow a standard normal distribution, find the values of the parameters that minimize a robust measure of their size. In practice an approximation of this transformation is used. The proposed estimators are studied theoretically for distributions that depend on a single parameter and through simulations and examples for the particular cases of Poisson and logistic regression.
ER  -