IMPROVING ESTIMATES OF MONOTONE FUNCTIONS BY REARRANGEMENT

Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon

No WP2007-012, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

Abstract: Suppose that a target function f0 : Rd ! R is monotonic, namely, weakly increasing, and an original estimate ^ f of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates ^ f. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate ^ f¤, and the resulting estimate is closer to the true curve f0 in common metrics than the original estimate ^ f. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

Keywords: Monotone function; improved approximation; multivariate rearrange- ment; univariate rearrangement; growth chart; quantile regression; mean regression; series; locally linear; kernel methods (search for similar items in EconPapers)
Pages: 31pages
Date: 2007-04
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (9)

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Related works:
Working Paper: Improving Estimates of Monotone Functions by Rearrangement (2010)
Working Paper: Improving estimates of monotone functions by rearrangement (2007)
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