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摘要翻译：
本文研究了高维近似稀疏回归的线性均方连续泛函的n根一致有效估计的能力和方法。这些对象包括各种有趣的参数，如两个回归残差之间的协方差、部分线性模型的系数、平均导数和平均处理效果。我们给出了这类对象的估计收敛速度的下界，并发现这些下界比低维半参数下的估计收敛速度大得多。我们也给出了在极小条件下$1/\sqrt{n}$一致且渐近有效的自动去偏机器学习器。这些估计器不使用交叉拟合或一种特殊的交叉拟合，以获得快于$n^{-1/4}$收敛的回归效率。这个速率条件比许多其他去偏机器学习器所要求的两个函数的收敛速度快于$1/\sqrt{n},$的乘积要弱得多。
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英文标题：
《Minimax Semiparametric Learning With Approximate Sparsity》
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作者：
Jelena Bradic, Victor Chernozhukov, Whitney K. Newey, Yinchu Zhu
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最新提交年份：
2021
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
This paper is about the ability and means to root-n consistently and efficiently estimate linear, mean square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters such as the covariance between two regression residuals, a coefficient of a partially linear model, an average derivative, and the average treatment effect. We give lower bounds on the convergence rate of estimators of such objects and find that these bounds are substantially larger than in a low dimensional, semiparametric setting. We also give automatic debiased machine learners that are $1/\sqrt{n}$ consistent and asymptotically efficient under minimal conditions. These estimators use no cross-fitting or a special kind of cross-fitting to attain efficiency with faster than $n^{-1/4}$ convergence of the regression. This rate condition is substantially weaker than the product of convergence rates of two functions being faster than $1/\sqrt{n},$ as required for many other debiased machine learners.
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PDF链接：
https://arxiv.org/pdf/1912.12213
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