High-dimensional statistical settings ($p \gg n$) pose fundamental challenges for classical inference, largely due to bias introduced by regularized estimators such as the LASSO. To address this, Javanmard and Montanari (2014) propose a debiased estimator that enables valid hypothesis testing and confidence interval construction. This report examines their debiased LASSO framework, which yields asymptotically normal estimators in high-dimensional settings. We present the key theoretical results underlying this approach, specifically, the construction of an optimized debiased estimator that restores asymptotic normality, which enables the computation of valid confidence intervals and $p$-values. To evaluate the claims of Javanmard and Montanari, a subset of the original simulation study and a re-examination of their real-data analysis are presented. Building on this baseline, we extend the empirical analysis to include the desparsified LASSO, a closely related method referenced but not implemented in the original study. The results demonstrate that while the debiased LASSO achieves reliable coverage and controls Type I error, the LASSO projection estimator can offer improved power in low-signal settings without compromising error rates. Our findings highlight a critical practical trade-off: while the LASSO projection estimator demonstrates superior statistical power in an idealized simulated low-signal setting, the estimation procedure employed by Javanmard and Montanari adapts more robustly to complex correlation networks, yielding superior precision and signal detection in real-world genomic data.

翻译：高维统计设定（$p \gg n$）为经典推断带来了根本性挑战，这主要源于LASSO等正则化估计量引入的偏差。为应对此问题，Javanmard与Montanari (2014)提出了一种去偏估计量，能够实现有效的假设检验和置信区间构建。本报告考察了其去偏LASSO框架，该框架可在高维设定下生成渐近正态估计量。我们阐述了支撑该方法的核心理论结果——具体而言，构建了一种优化的去偏估计量以恢复渐近正态性，从而能够计算有效的置信区间和$p$值。为评估Javanmard与Montanari的论断，我们呈现了原仿真研究的部分复现结果，并重新审视了其真实数据分析。在此基准上，我们将实证分析扩展至去稀疏化LASSO方法——该密切相关的技术在原始研究中提及但未予实现。结果表明：去偏LASSO虽能实现可靠覆盖并控制第一类错误，但LASSO投影估计量在低信号设定下可在不牺牲错误率的前提下提升统计功效。我们的发现揭示了一个关键的实践权衡：LASSO投影估计量在理想化仿真的低信号设定中展现出更强的统计功效，而Javanmard与Montanari采用的估计程序能更鲁棒地适应复杂相关网络，从而在真实基因组数据中实现更优的精度与信号检测能力。