arXiv 28 Nov 2020 · Mathematics — Statistics Theory · 3 citations (OpenAlex)
arXiv:2011.14219 · PDF · DOI · OpenAlex · Extracted main text
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some or all of the arguments. We derive the minimax rate of convergence for confidence intervals (CIs) that adapt to the underlying smoothness, and provide an adaptive inference procedure that obtains this minimax rate. The procedure differs from that of Cai and Low (2004), intended to yield shorter CIs under practically relevant specifications. The proposed method applies to general linear functionals of the regression function, and is shown to have favorable performance compared to existing inference procedures.
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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 | Cai, T. T. and M. G. Low (2004) An Adaptation Theory for Nonparametric Confidence Intervals | 1.000 | 24 | 5 | 100% |
| 2 | Armstrong, T. B. and M. Kolesár (2018) Optimal Inference in a Class of Regression Models | 0.961 | 9 | 3 | 89% |
| 3 | Donoho, D. L (1994) Statistical Estimation and Optimal Recovery | 0.644 | 2 | 2 | 100% |
| 4 | Armstrong, T (2015) Adaptive Testing on a Regression Function at a Point | 0.511 | 2 | 1 | 100% |
| 5 | Cai, T. T., M. G. Low, and Y. Xia (2013) Adaptive Confidence Intervals for Regression Functions under Shape Constraints | 0.511 | 2 | 1 | 100% |
| 6 | Horowitz, J. L. and S. Lee (2017) Nonparametric Estimation and Inference Under Shape Restrictions | 0.511 | 2 | 1 | 100% |
| 7 | Low, M. G (1997) On Nonparametric Confidence Intervals | 0.511 | 2 | 1 | 100% |
| 8 | Beliakov, G (2005) Monotonicity Preserving Approximation of Multivariate Scattered Data | 0.405 | 1 | 1 | 100% |
| 9 | Cai, T. T. and M. G. Low (2006) Adaptive Confidence Balls | 0.405 | 1 | 1 | 100% |
| 10 | Cai, T. T (2012) Minimax and Adaptive Inference in Nonparametric Function Estimation | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Short and Simple Confidence Intervals when the Directions of Some Effects are Known | 0.874 | 5 | 2 |
| 2 | Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs | 0.405 | 1 | 1 |