基础数学系学术报告

题目: Debiased and thresholded ridge regression for linear models with heterogeneous and correlated errors

报告人: 张云翼（香港中文大学（深圳））

时间：2022-03-17 15:00-17:00 (周五下午)

地点: 沙河E404

摘要: 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 non-stationary) errors is still a novel topic. Under such complex assumptions, this presentation 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 heterogeneous, (weakly) dependent, and non-stationary random variables that can be used as a general model for regression errors.

报告人简介: 张云翼, 香港中文大学（深圳）助理教授，博士生导师。2022年6月获得加利福尼亚大学圣地亚哥分校数学（统计学）博士学位，于同年8月就职于香港中文大学（深圳）。报告人主要从事统计学及相关领域的研究，包括非平稳时间序列分析，重抽样方法，高维统计等。报告人主要科研成果发表在Annals of Statistics，Information and Inference: A Journal of the IMA, Electronic Journal of Statistics等高水平的国际期刊上。

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