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摘要翻译：
在具有同方差的高维稀疏中值回归模型中，建立了回归系数的一致有效置信域。我们的方法是基于一个矩方程，该矩方程通过Neyman正交化对中值回归函数的干扰部分进行非正则估计。我们证明了目标回归系数的工具中值回归估计相对于底层稀疏模型是渐近正态分布一致的，并且是半参数有效的。我们还将我们的方法推广到一个一般的非光滑Z-估计框架，目标参数的数目$P_1$可能远大于样本量$N$。我们将Huber关于渐近正态性的结果推广到这种情形，证明了所提出的估计量在$P1$维矩形上的一致渐近正态性，在所有$P1$目标参数上构造了同时置信带，并在近似稀疏模型上建立了一致置信带的渐近有效性。关键词：仪器；选择后推理；稀疏性；尼曼正交评分试验；一致有效推论；Z-估计。
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英文标题：
《Uniform Post Selection Inference for LAD Regression and Other
Z-estimation problems》
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作者：
Alexandre Belloni and Victor Chernozhukov and Kengo Kato
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最新提交年份：
2020
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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：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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：
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular estimation of the nuisance part of the median regression function by using Neyman's orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed uniformly with respect to the underlying sparse model and is semi-parametrically efficient. We also generalize our method to a general non-smooth Z-estimation framework with the number of target parameters $p_1$ being possibly much larger than the sample size $n$. We extend Huber's results on asymptotic normality to this setting, demonstrating uniform asymptotic normality of the proposed estimators over $p_1$-dimensional rectangles, constructing simultaneous confidence bands on all of the $p_1$ target parameters, and establishing asymptotic validity of the bands uniformly over underlying approximately sparse models. Keywords: Instrument; Post-selection inference; Sparsity; Neyman's Orthogonal Score test; Uniformly valid inference; Z-estimation.
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PDF链接：
https://arxiv.org/pdf/1304.0282
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