# Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach

arXiv: https://arxiv.org/abs/1903.04408 · HTML: https://mlsanity.com/paper/1903.04408/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 6 of 6)

- [Best-Subset Selection in Generalized Linear Models: A Fast and Consistent Algorithm via Splicing Technique](https://mlsanity.com/paper/2308.00251/) (2023)
- [Inference for High Dimensional Censored Quantile Regression](https://mlsanity.com/paper/2107.10959/) (2021)
- [A Model-free Closeness-of-influence Test for Features in Supervised Learning](https://mlsanity.com/paper/2306.11855/) (2023)
- [U-learning for Prediction Inference via Combinatory Multi-Subsampling: With Applications to LASSO and Neural Networks](https://mlsanity.com/paper/2407.15301/) (2024)
- [An Overview of Healthcare Data Analytics With Applications to the COVID-19 Pandemic](https://mlsanity.com/paper/2111.14623/) (2021)
- [Kernel-Based Learning of Chest X-ray Images for Predicting ICU Escalation among COVID-19 Patients](https://mlsanity.com/paper/2602.10261/) (2026)

## Abstract (arXiv)

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strategies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a "splitting and smoothing" approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.