LARGE SAMPLE PROPERTIES OF PARTITIONING-BASED SERIES ESTIMATORS

• 成果类型: Article
• 署名作者: Cattaneo, Matias D.; Farrell, Max H.; Feng, Yingjie
• 署名单位: Princeton University; University of Chicago; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1865
• 发表日期: 2020
• 页码: 1718-1741
• 关键词: Asymptotic Normality; convergence-rates; Gaussian Approximation; local asymptotics; partial sums; regression; suprema

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 point-wise 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.