Matias D. Cattaneo, Max H. Farrell, Yingjie Feng
arXiv 13 Apr 2018 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2020) · 46 citations (OpenAlex)
arXiv:1804.04916 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | barticle[author] Cattaneo, Matias D.M. D. Farrell, Max H.M. H (2013) ) self | 1.000 | 5 | 3 | 100% |
| 2 | barticle[author] Barrow, D. L.D. L. Smith, P. W.P. W (1978) ) | 0.928 | 4 | 3 | 100% |
| 3 | bbook[author] Schumaker, LarryL (2007) ) | 0.874 | 6 | 2 | 100% |
| 4 | barticle[author] Belloni, AlexandreA., Chernozhukov, VictorV., Chetv… (2015) ) | 0.874 | 5 | 2 | 100% |
| 5 | barticle[author] Sweldens, WimW. Piessens, RobertR (1994) ) | 0.737 | 3 | 2 | 100% |
| 6 | barticle[author] Agarwal, Girdhar GG. G. Studden, WJW (1980) ) | 0.644 | 2 | 2 | 100% |
| 7 | barticle[author] Cattaneo, Matias D.M. D., Farrell, Max H.M. H. Feng… (2019) ) self | 0.644 | 2 | 2 | 100% |
| 8 | barticle[author] Zhou, ShanggangS. Wolfe, Douglas AD. A (2000) ) | 0.644 | 2 | 2 | 100% |
| 9 | bbook[author] Bhatia, RajendraR (2013) ) | 0.511 | 2 | 1 | 100% |
| 10 | barticle[author] Cohen, AlbertA., Daubechies, IngridI. Vial, PierreP (1993) ) | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 28 scored citations.
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