发表机构
Waseda University（早稻田大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于平滑重参数化映射的统一正则化框架，将稀疏性嵌入参数变换，实现高维M-估计的oracle渐近正态性，并在线性与Cox模型中优于或媲美SCAD和MCP。
AI 中文摘要
本文建立了一个统一的高维$M$-估计的非线性正则化框架，涵盖线性模型和Cox比例风险模型。与依赖传统加性非凸惩罚（其带来严重的优化挑战）不同，所提出的范式通过平滑（$C^2$）逐分量“稀疏重参数化映射（RePS）”$\phi^{(\nu)}$，将稀疏性直接嵌入物理参数$\theta=\phi^{(\nu)}(\beta)$的变换中，且惩罚项为$\lambda \Vert \beta \Vert_1$而非$\lambda \Vert \theta \Vert_1$。这种结构公式动态适应局部参数尺度，抑制高维噪声，同时在大样本极限下恢复无偏的oracle渐近正态性。通过原始-对偶见证方法，我们在维度相关的对数缩放$n^{-1/2} \ll \nu \leq \log p$下，为两类模型建立了统一的oracle等价性，并明确适应模型特定结构，如生存分析中的平移不变性。大量蒙特卡洛模拟表明，所提出的框架在高维线性模型中始终实现优越的假阳性控制和高的95%置信区间覆盖率，同时在比例风险模型中，在所有方面均达到与SCAD和MCP等最先进方法相当或更优的性能。
英文摘要
This paper establishes a unified non-linear regularization framework for high-dimensional $M$-estimation, encompassing both linear models and Cox's proportional hazards models. Rather than relying on traditional additive non-convex penalties, the proposed paradigm embeds sparsity directly into the transformation for the physical parameter $θ=ϕ(β)$ using a smooth ($C^2$) component-wise "ReParametrization map for Sparsity (RePS)" $ϕ$, and the penalty term is $λ\Vert β\Vert_1$ rather than $λ\Vert θ\Vert_1$. This structural formulation dynamically adapts to local parameter scales, suppressing high-dimensional noise while simultaneously recovering unbiased oracle asymptotic normality under the large-sample limit. Through the Primal-Dual Witness method, we establish a unified oracle equivalence for both model classes under a liberated micro-penalty scaling regime $λ\ll n^{-1/2}$, accommodating model-specific structures such as the shift-invariance in survival analysis. Extensive Monte Carlo simulations demonstrate that the proposed framework consistently achieves superior false-positive control and high 95\% confidence interval coverage in high-dimensional linear models, while also delivering performance comparable or superior in all aspects to state-of-the-art methods like SCAD and MCP in proportional hazards models.
Comments18 pages
