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Improving Point and Interval Estimates of Monotone Functions by Rearrangement

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

Abstract

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.

Citation extraction

38
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46
in-text mentions
38
distinct cited
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7,797
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Dette and Scheder (2006) Strictly monotone and smooth nonparametric regression for two or more variables0.73732100%
2Mammen (1991) Nonparametric Regression Under Qualitative Smoothness Assumptions0.64422100%
3Dette, Neumeyer, and Pilz (2006) A simple nonparametric estimator of a strictly monotone regression function0.64422100%
4Lorentz (1953) An inequality for rearrangements0.64422100%
5Wei, Pere, Koenker, and He (2006) Quantile regression methods for reference growth charts0.51121100%
6Chernozhukov, Fernandez-Val, and Galichon (2006) Rearranging Edgeworth-Cornish-Fisher Expansions self0.40511100%
7Davydov and Zitikis (2005) An index of monotonicity and its estimation: a step beyond econometric applications of the Gini index0.40511100%
8Genovese and Wasserman (2008) Adaptive confidence bands0.40511100%
9Hardy, Littlewood, and Pólya (1952) Inequalities0.40511100%
10Hall (1993) On Edgeworth Expansion and Bootstrap Confidence Bands in Nonparametric Curve Estimation0.40511100%

Showing the top 10 of 38 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1A Unifying Framework for Testing Shape Restrictions0.81142