Improving Estimates Of Monotone Functions By Rearrangement
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.
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| Length: | 31pages |
| Date of creation: | Apr 2007 |
| Date of revision: | |
| Handle: | RePEc:bos:wpaper:wp2007-012 |
| Contact details of provider: | Postal: 270 Bay State Road, Boston, MA 02215 Phone: 617-353-4389 Fax: 617-353-4449 Web page: http://www.bu.edu/econ/ More information through EDIRC
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