Deep non-parametric logistic model with case-control data and external summary information
<|reference_start|>Deep non-parametric logistic model with case-control data and external summary information: The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.<|reference_end|>
@article{shi2024deep,
    title={Deep non-parametric logistic model with case-control data and external
  summary information},
    author={Hengchao Shi, Ming Zheng, Wen Yu},
    journal={arXiv preprint arXiv:2409.01829},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01829},
    primaryClass={stat.ML cs.LG}
}