高维分位数变化点的Oracle估计 回归

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摘要翻译：
在本文中，我们考虑了一个高维分位数回归模型，其中两个子种群之间的稀疏结构可能不同。我们给出了回归系数和阈值参数的$\ell_1$-惩罚估计。我们的惩罚估计不仅选择协变量，而且区分具有齐次稀疏性的模型和具有变点的模型。因此，不需要知道或预先测试变化点是否存在，或者它发生在哪里。我们的变点估计得到了一个oracle性质，即它的渐近分布与已知的未知回归系数活动集相同。重要的是，我们在没有完美协变量选择的情况下建立了这个oracle属性，从而避免了对活动协变量信号的最小水平条件的需要。对于带有未知变点的高维分位数回归，由于分位数损失函数是非光滑的，而且相应的目标函数相对于变点是非凸的，需要一种新的证明技术。本文所发展的技术适用于具有变点的一般M-估计框架，这可能是独立感兴趣的。然后通过蒙特卡罗实验和在种族隔离动力学中的一个应用来说明所提出的方法。
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英文标题：
《Oracle Estimation of a Change Point in High Dimensional Quantile
  Regression》
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作者：
Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin
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最新提交年份：
2016
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分类信息：

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：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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英文摘要：
  In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs. Our estimator of the change point achieves an oracle property in the sense that its asymptotic distribution is the same as if the unknown active sets of regression coefficients were known. Importantly, we establish this oracle property without a perfect covariate selection, thereby avoiding the need for the minimum level condition on the signals of active covariates. Dealing with high-dimensional quantile regression with an unknown change point calls for a new proof technique since the quantile loss function is non-smooth and furthermore the corresponding objective function is non-convex with respect to the change point. The technique developed in this paper is applicable to a general M-estimation framework with a change point, which may be of independent interest. The proposed methods are then illustrated via Monte Carlo experiments and an application to tipping in the dynamics of racial segregation.
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PDF链接：
https://arxiv.org/pdf/1603.00235

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关键词：Oracle CLE ACL 分位数 econometrics 位数 变量 需要 between dimensional