Debiased and thresholded ridge regression for linear models with heteroskedastic and correlated errors
针对高维线性模型中误差存在异方差、相关甚至非平稳的情况，提出一种无偏且带阈值的岭回归估计量，能恢复模型稀疏性，并给出高斯近似定理和自助法构造置信区间与假设检验，模拟和真实数据表现良好。
Abstract High-dimensional linear models with independent errors have been well-studied. However, statistical inference on a high-dimensional linear model with heteroskedastic, dependent (and possibly nonstationary) errors is still a novel topic. Under such complex assumptions, the paper at hand introduces a debiased and thresholded ridge regression estimator that is consistent, and is able to recover the model sparsity. Moreover, we derive a Gaussian approximation theorem for the estimator, and apply a dependent wild bootstrap algorithm to construct simultaneous confidence interval and hypothesis tests for linear combinations of parameters. Numerical experiments with both real and simulated data show that the proposed estimator has good finite sample performance. Of independent interest is the development of a new class of heteroscedastic, (weakly) dependent, and nonstationary random variables that can be used as a general model for regression errors.