Improving point and interval estimates of monotone functions by rearrangement
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 of creation:||Jul 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.ukEmail:
More information through EDIRC
|Order Information:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007.
"Improving Estimates Of Monotone Functions By Rearrangement,"
Boston University - Department of Economics - Working Papers Series
WP2007-012, Boston University - Department of Economics.
- 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.
- Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
- Youri Davydov & Ricardas Zitikis, 2005. "An index of monotonicity and its estimation: a step beyond econometric applications of the Gini index," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 351-372.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
- Donald W.K. Andrews, 1988.
"Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models,"
Cowles Foundation Discussion Papers
874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
- Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March.
- Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558 Elsevier.
When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:17/08. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stephanie Seavers)
If references are entirely missing, you can add them using this form.