摘要翻译：
我们给出了基于划分的最小二乘非参数回归的大样本结果，这是一种在统计学、计量经济学和机器学习中逼近条件期望函数的流行方法。首先，我们得到了它们的超前渐近偏置的一般刻划。其次，我们建立了积分均方误差逼近的点估计，并提出了可行的调整参数选择。第三，我们发展了基于欠平滑和鲁棒偏差校正的逐点推理方法。第四，利用不同的耦合方法，我们对欠平滑和鲁棒偏差校正的t-统计量过程建立了一致的分布近似，并构造了有效的置信带。在单变量情况下，我们的均匀分布近似要求似乎最小的速率限制，并改进了文献中已知的近似速率。最后，我们将我们的一般结果应用于三种基于划分的估计：样条、小波和分段多项式。补充附录包括其他几个一般性和具体实例的技术和方法学结果。提供了配套的R包。
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英文标题：
《Large Sample Properties of Partitioning-Based Series Estimators》
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作者：
Matias D. Cattaneo, Max H. Farrell, Yingjie Feng
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最新提交年份：
2019
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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：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 present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop pointwise inference methods based on undersmoothing and robust bias correction. Fourth, employing different coupling approaches, we develop uniform distributional approximations for the undersmoothed and robust bias-corrected t-statistic processes and construct valid confidence bands. In the univariate case, our uniform distributional approximations require seemingly minimal rate restrictions and improve on approximation rates known in the literature. Finally, we apply our general results to three partitioning-based estimators: splines, wavelets, and piecewise polynomials. The supplemental appendix includes several other general and example-specific technical and methodological results. A companion R package is provided.
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PDF链接：
https://arxiv.org/pdf/1804.04916