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. The key theoretical results underlying this approach are presented. 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 the real-data analysis is presented. The original empirical analysis is extended to the desparsified LASSO, which is 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 idealized low-signal settings without compromising error rates. The results reveal a trade-off: the LASSO projection estimator performs well in low-signal settings, while Javanmard and Montanari's method is more robust to complex correlations, improving precision and signal detection in real data.

翻译：高维统计设定（$p \gg n$）对经典推断构成了根本性挑战，这主要源于LASSO等正则化估计量引入的偏差。为解决该问题，Javanmard与Montanari（2014）提出了一种去偏估计量，使得有效的假设检验和置信区间构建成为可能。本报告考察了他们的去偏LASSO框架，该框架能在高维设定下生成渐近正态的估计量。文中阐述了该方法背后的关键理论结果，具体包括：通过构建优化后的去偏估计量恢复渐近正态性，进而实现有效置信区间与$p$值的计算。为验证Javanmard与Montanari的主张，本研究复现了原始研究的部分模拟实验和真实数据分析，并将原始实证分析扩展至原始文献中提及但未实施的去稀疏化LASSO（desparsified LASSO）。结果表明，去偏LASSO能实现可靠的覆盖率和I类错误控制，而在理想化低信号设定下，LASSO投影估计量可在不牺牲错误率的前提下提供更高的统计功效。结果揭示了权衡关系：LASSO投影估计量在低信号场景中表现优异，而Javanmard与Montanari的方法对复杂相关性更具稳健性，从而在真实数据中提升了精度和信号检测能力。