We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized estimation settings. The conditions are weak and accommodate a broad class of estimation problems, including ones with non-convex and group structured penalties. The wide applicability of the results is illustrated through diverse examples, including generalized linear models, multi-sample inference, and stepwise estimation procedures.

翻译：本文研究高维估计问题，其中参数数量随样本量发散。我们建立了无惩罚估计与惩罚估计场景下一致性、唯一性及渐近正态性的一般性条件。这些条件具有弱约束性，适用于包括非凸惩罚与分组结构惩罚在内的广泛估计问题。通过广义线性模型、多样本推断及逐步估计程序等多样化示例，展示了研究结果的广泛适用性。