摘要翻译：
本文研究了在有限内存约束下，当样本容量为n$时，分位数回归(QR)中的推理问题，其中内存只能存储M$的小批数据。一种自然的方法是NA\\“ive divide-and-conquer方法，它将数据分成大小为$M$的批，为每批计算局部QR估计量，然后通过平均聚合估计量。但是，此方法只在$n=O(m^2)$时工作，并且计算开销很大。本文提出了一种计算效率较高的方法，该方法只需对小批数据进行初始QR估计，然后通过多轮聚合对估计进行连续精化。理论上，只要N$以M$为多项式增长，我们就建立了所得到的估计量的渐近正态性，并且证明了我们的估计量只需几轮聚合就能达到与QR估计量在所有数据上计算相同的效率。此外，我们的结果允许维数$P$到无穷大的情况。该方法也可以应用于分布式计算环境（例如，在大规模传感器网络中）或实时流数据中的QR问题。
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英文标题：
《Quantile Regression Under Memory Constraint》
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作者：
Xi Chen, Weidong Liu, Yichen Zhang
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最新提交年份：
2018
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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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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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英文摘要：
  This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\"ive divide-and-conquer approach, which splits data into batches of size $m$, computes the local QR estimator for each batch, and then aggregates the estimators via averaging. However, this method only works when $n=o(m^2)$ and is computationally expensive. This paper proposes a computationally efficient method, which only requires an initial QR estimator on a small batch of data and then successively refines the estimator via multiple rounds of aggregations. Theoretically, as long as $n$ grows polynomially in $m$, we establish the asymptotic normality for the obtained estimator and show that our estimator with only a few rounds of aggregations achieves the same efficiency as the QR estimator computed on all the data. Moreover, our result allows the case that the dimensionality $p$ goes to infinity. The proposed method can also be applied to address the QR problem under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.
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PDF链接：
https://arxiv.org/pdf/1810.08264