{"ID":23474945,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19558","arxiv_id":"2609.19558","title":"Oracle high-dimensional $M$-estimation using smooth reparameterization for sparsity","abstract":"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 which pose severe optimization challenges, the proposed paradigm embeds sparsity directly into the transformation for the physical parameter $θ=φ^{(ν)}(β)$ using a smooth ($C^2$) component-wise \"ReParametrization map for Sparsity (RePS)\" $φ^{(ν)}$, 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 dimension-dependent logarithmic scaling $n^{-1/2} \\ll ν\\leq \\log p$, explicitly 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.","short_abstract":"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 which pose severe optimization challenges, the proposed paradigm embeds sparsi...","url_abs":"https://arxiv.org/abs/2609.19558","url_pdf":"https://arxiv.org/pdf/2609.19558v1","authors":"[\"Yoichi Nishiyama\"]","published":"2026-09-17T01:35:44Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}