Victor Chernozhukov, Ivan Fernandez-Val, Alfred Galichon
arXiv 29 Jun 2008 · Mathematics — Statistics Theory · 21 citations (OpenAlex)
arXiv:0806.4730 · PDF · DOI · OpenAlex · Extracted main text
Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original simultaneous confidence interval, which covers the target function with probability at least $1-α$, is defined by an upper and lower end-point functions that are not weakly increasing. Then the rearranged confidence interval, defined by the rearranged upper and lower end-point functions, is shorter in length in common norms than the original interval and also covers the target function with probability at least $1-α$. We demonstrate the utility of the improved point and interval estimates with an age-height growth chart example.
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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 | Dette and Scheder (2006) Strictly monotone and smooth nonparametric regression for two or more variables | 0.737 | 3 | 2 | 100% |
| 2 | Mammen (1991) Nonparametric Regression Under Qualitative Smoothness Assumptions | 0.644 | 2 | 2 | 100% |
| 3 | Dette, Neumeyer, and Pilz (2006) A simple nonparametric estimator of a strictly monotone regression function | 0.644 | 2 | 2 | 100% |
| 4 | Lorentz (1953) An inequality for rearrangements | 0.644 | 2 | 2 | 100% |
| 5 | Wei, Pere, Koenker, and He (2006) Quantile regression methods for reference growth charts | 0.511 | 2 | 1 | 100% |
| 6 | Chernozhukov, Fernandez-Val, and Galichon (2006) Rearranging Edgeworth-Cornish-Fisher Expansions self | 0.405 | 1 | 1 | 100% |
| 7 | Davydov and Zitikis (2005) An index of monotonicity and its estimation: a step beyond econometric applications of the Gini index | 0.405 | 1 | 1 | 100% |
| 8 | Genovese and Wasserman (2008) Adaptive confidence bands | 0.405 | 1 | 1 | 100% |
| 9 | Hardy, Littlewood, and Pólya (1952) Inequalities | 0.405 | 1 | 1 | 100% |
| 10 | Hall (1993) On Edgeworth Expansion and Bootstrap Confidence Bands in Nonparametric Curve Estimation | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 38 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Unifying Framework for Testing Shape Restrictions | 0.811 | 4 | 2 |