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置下广泛广义线性模型的统计推断方法，其中未知系数数量与样本量成比例增长。尽管逻辑回归（广义线性模型的一个特例）已存在开创性方法，但其直接应用于其他广义线性模型仍存在局限。本研究通过为具有非对称连接函数的一类广义线性模型设计新推断方法，解决了这一局限。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系统，这是推断的关键组成部分。接着，我们设计了一种方法以识别该方法所需系统中的参数。在此基础上，我们构建了高维广义线性模型的置信区间。我们证明了所提方法具有强相合性与精确覆盖概率等理想理论性质。最后，我们通过实验验证了其有效性。