Large sample properties of partitioning-based series estimators
Large sample properties of partitioning-based series estimators
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DOI：
10.1214/19-aos1865
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
M. D. Cattaneo;M. Farrell;Yingjie Feng
中科院分区：
文献类型：
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作者：
M. D. Cattaneo;M. Farrell;Yingjie Feng
我们展示了基于分割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近似条件期望函数的流行方法。首先，我们得到了它们的主要渐近偏差的一般表征。其次，建立了点估计器的积分均方误差近似，并提出了可行的整定参数选择。第三，我们开发了基于欠平滑和鲁棒偏差校正的点推理方法。第四，采用不同的耦合方法，我们为欠平滑和稳健偏差校正的t统计过程建立了均匀分布近似，并构建了有效的置信带。在单变量情况下，我们的均匀分布近似要求看似最小的速率限制，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分割的估计：样条，小波和分段多项式。补充附录包括其他几个一般和特定示例的技术和方法结果。提供了一个配套的R包。
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.