In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional Ito diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or instantaneous) coefficients using a time-localized Dantzig selection scheme under a sparsity condition, which results in biased local coefficient estimators due to the regularization. To handle the bias, we propose a debiasing scheme, which provides well-performing unbiased local coefficient estimators. With the unbiased local coefficient estimators, we estimate the integrated coefficient, and to further account for the sparsity of the coefficient process, we apply thresholding schemes. We call this Thresholding dEbiased Dantzig (TED). We establish asymptotic properties of the proposed TED estimator. In the empirical analysis, we apply the TED procedure to analyzing high-dimensional factor models using high-frequency data.

翻译：本文提出了一种基于高维伊藤扩散过程的新型高维时变系数估计方法。为处理高维时变系数，我们首先在稀疏性条件下利用时间局部化的Dantzig选择方案估计局部（或瞬时）系数，但由于正则化处理，该方法会导致局部系数估计产生偏差。针对该偏差问题，我们提出了一种去偏方案，能够获得性能良好的无偏局部系数估计量。基于无偏局部系数估计量，我们进一步估计积分系数，并通过对系数过程施加阈值处理方案来保持稀疏性。我们将此方法命名为阈值去偏Dantzig估计器（TED）。我们建立了所提出TED估计量的渐近性质。在实证分析中，我们将TED方法应用于高频数据下的高维因子模型分析。