Xi Chen, Victor Chernozhukov, Iván Fernández-Val, Scott Kostyshak, Ye Luo
arXiv 4 Sep 2018 · Econometrics · 5 citations (OpenAlex)
arXiv:1809.01038 · PDF · DOI · OpenAlex · Extracted main text
A common problem in econometrics, statistics, and machine learning is to estimate and make inference on functions that satisfy shape restrictions. For example, distribution functions are nondecreasing and range between zero and one, height growth charts are nondecreasing in age, and production functions are nondecreasing and quasi-concave in input quantities. We propose a method to enforce these restrictions ex post on point and interval estimates of the target function by applying functional operators. If an operator satisfies certain properties that we make precise, the shape-enforced point estimates are closer to the target function than the original point estimates and the shape-enforced interval estimates have greater coverage and shorter length than the original interval estimates. We show that these properties hold for six different operators that cover commonly used shape restrictions in practice: range, convexity, monotonicity, monotone convexity, quasi-convexity, and monotone quasi-convexity. We illustrate the results with two empirical applications to the estimation of a height growth chart for infants in India and a production function for chemical firms in China.
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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 | Victor Chernozhukov, Iván Fernández-Val, and Alfred Galichon (2009) Improving point and interval estimators of monotone functions by rearrangement self | 1.000 | 7 | 3 | 100% |
| 2 | RE Barlow, DJ Bartholomew, JM Bremner, and HD Brunk (1972) Statistical inference under order restrictions | 0.843 | 3 | 3 | 100% |
| 3 | Joel L Horowitz and Sokbae Lee (2017) Nonparametric estimation and inference under shape restrictions | 0.737 | 3 | 2 | 100% |
| 4 | Denis Chetverikov, Andres Santos, and Azeem M Shaikh (2018) The econometrics of shape restrictions | 0.737 | 3 | 2 | 100% |
| 5 | Roger Koenker and Ivan Mizera (2010) Quasi-concave density estimation | 0.644 | 2 | 2 | 100% |
| 6 | Victor Chernozhukov, Denis Chetverikov, and Kengo Kato Anti-concentration and honest, adaptive confidence bands self | 0.644 | 2 | 2 | 100% |
| 7 | Evarist Giné and Richard Nickl (2010) Confidence bands in density estimation | 0.644 | 2 | 2 | 100% |
| 8 | Brendan K Beare and Zheng Fang (2017) Weak convergence of the least concave majorant of estimators for a concave distribution function | 0.585 | 3 | 1 | 100% |
| 9 | Lutz Dümbgen (2003) Optimal confidence bands for shape-restricted curves | 0.585 | 3 | 1 | 100% |
| 10 | Adityanand Guntuboyina and Bodhisattva Sen (2018) Nonparametric shape-restricted regression | 0.585 | 3 | 1 | 100% |
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