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Improving point and interval estimators of monotone functions by rearrangement

  • V. Chernozhukov
  • I. Fernández-Val
  • A. Galichon

Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-α, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-α. We illustrate the results with a growth chart example. Copyright 2009, Oxford University Press.

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Article provided by Biometrika Trust in its journal Biometrika.

Volume (Year): 96 (2009)
Issue (Month): 3 ()
Pages: 559-575

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Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:559-575
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  1. 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.
  2. 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.
  3. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  4. 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.
  5. 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.
  6. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
  7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  8. 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.
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