Debiased inference for high-dimensional regression models has received substantial recent attention to ensure regularized estimators have valid inference. All existing methods focus on achieving Neyman orthogonality through explicitly constructing projections onto the space of nuisance parameters, which is infeasible when an explicit form of the projection is unavailable. We introduce a general debiasing framework, Debiased Profile M-Estimation (DPME), which applies to a broad class of models and does not require model-specific Neyman orthogonalization or projection derivations as in existing methods. Our approach begins by obtaining an initial estimator of the parameters by optimizing a penalized objective function. To correct for the bias introduced by penalization, we construct a one-step estimator using the Newton-Raphson update, applied to the gradient of a profile function defined as the optimal objective function with the parameter of interest held fixed. We use numerical differentiation without requiring the explicit calculation of the gradients. The resulting DPME estimator is shown to be asymptotically linear and normally distributed. Through extensive simulations, we demonstrate that the proposed method achieves better coverage rates than existing alternatives, with largely reduced computational cost. Finally, we illustrate the utility of our method with an application to estimating a treatment rule for multiple myeloma.

翻译：高维回归模型的去偏推断近年来受到广泛关注，以确保正则化估计量具备有效的推断性质。现有方法均侧重于通过显式构建对干扰参数空间的投影来实现Neyman正交性，但当投影的显式形式不可得时，该方法不可行。本文提出一种通用的去偏框架——去偏轮廓M估计（DPME），该框架适用于广泛的模型类别，且无需如现有方法般进行模型特定的Neyman正交化或投影推导。我们的方法首先通过优化惩罚目标函数获得参数的初始估计量。为修正惩罚引入的偏差，我们采用牛顿-拉弗森更新构建一步估计量，该更新作用于轮廓函数的梯度——该函数定义为在固定目标参数时最优化的目标函数。我们使用数值微分方法，无需显式计算梯度。理论证明所得DPME估计量具有渐近线性与正态分布特性。通过大量模拟实验，我们证明所提方法相较于现有替代方案具有更优的覆盖概率，且计算成本显著降低。最后，我们通过多发性骨髓瘤治疗规则的估计案例展示了本方法的实用价值。