We have developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a pioneering method has been developed for logistic regression, which is a specific instance of GLMs, its direct applicability to other GLMs remains limited. In this study, we address this limitation by developing a new inference method designed for a class of GLMs with asymmetric link functions. More precisely, we first introduce a novel convex loss-based estimator and its associated system, which are essential components for the inference. We next devise a methodology for identifying parameters of the system required within the method. Consequently, we construct confidence intervals for GLMs in the high-dimensional regime. We prove that our proposal has desirable theoretical properties, such as strong consistency and exact coverage probability. Finally, we confirm the validity in experiments.

翻译：我们开发了一种适用于高维设定下广泛广义线性模型类的统计推断方法，其中未知系数数量与样本量成比例增长。尽管已有针对逻辑回归（广义线性模型的特例）的开拓性方法，但其对其他广义线性模型的直接适用性仍然有限。本研究通过为具有非对称链接函数的广义线性模型类设计新推断方法，解决了这一局限性。具体而言，我们首先引入了一种基于凸损失的新型估计量及其关联方程组，这是推断方法的核心组件。随后我们设计了识别该方法所需方程组参数的策略，从而在高维场景下构建了广义线性模型的置信区间。我们证明该方案具有强相合性和精确覆盖概率等理想理论性质，最后通过实验验证了其有效性。