Double debiased estimation and inference for longitudinal generalized linear models with hidden confounders

• Published in: Statistics and computing Vol. 35; no. 5
• Main Authors: Fei, Yuxin, Liu, Jin, Wang, Lei
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.10.2025
• Subjects: Air quality; Asymptotic methods; Dimensional analysis; Generalized linear models; Generalized method of moments; Maximum likelihood estimation; Normality; Statistical inference; Statistical models
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-025-10645-3

The hidden confounding model has been widely applied in many fields. Without adjusting for the hidden confounders, the estimators from the standard methods of high-dimensional models could be biased. In this paper, we focus the estimation and statistical inference on a preconceived low-dimensional parameter of main interest for high-dimensional longitudinal generalized linear models with hidden confounders. To handle the impact of the hidden confounders and high-dimensional nuisance covariates in longitudinal data simultaneously, a two-stage deconfounded and debiased (DD) estimator is proposed, which achieves the double debiased estimation. In the first stage, we impute the hidden confounders by high-dimensional factor model analysis techniques and maximum likelihood estimation. In the second stage, we construct the quasi decorrelated score function and obtain the DD estimator by the two-step generalized method of moment approach. Theoretically, the error bounds and the asymptotic normality of our proposed estimator are established. Our method shows good finite sample performance in simulation studies. An application to the Beijing Air Quality Dataset is also presented.