Improving point and interval estimates of monotone functions by rearrangement

Victor Chernozhukov, Ivan Fernandez-Val () and Alfred Galichon

No CWP17/08, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract:

Suppose that a target function is monotonic, namely weakly increasing, and an original estimate of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm by using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. The improvement property of the rearrangement also extends to the construction of confidence bands for monotone functions. Let l and u be the lower and upper endpoint functions of a simultaneous confidence interval [l,u] that covers the true function with probability (1-a), then the rearranged confidence interval, defined by the rearranged lower and upper end-point functions, is shorter in length in common norms than the original interval and covers the true function with probability greater or equal to (1-a). We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

Please note: This paper is a revised version of cemmap working Paper CWP09/07.

Date: 2008-07-06
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://cemmap.ifs.org.uk/wps/cwp1708.pdf (application/pdf)

Related works:
Journal Article: Improving point and interval estimators of monotone functions by rearrangement (2009)
Working Paper: Improving point and interval estimators of monotone functions by rearrangement (2009)
Working Paper: Improving point and interval estimators of monotone functions by rearrangement (2009)
Working Paper: Improving Point and Interval Estimates of Monotone Functions by Rearrangement (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:17/08

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().