Improving Estimates Of Monotone Functions By Rearrangement
AbstractSuppose 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.
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Bibliographic InfoPaper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2007-012.
Date of creation: Apr 2007
Date of revision:
Monotone function; improved approximation; multivariate rearrange- ment; univariate rearrangement; growth chart; quantile regression; mean regression; series; locally linear; kernel methods;
Other versions of this item:
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving estimates of monotone functions by rearrangement," CeMMAP working papers CWP09/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007.
"Rearranging Edgeworth-Cornish-Fisher expansions,"
CeMMAP working papers
CWP19/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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