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Asymptotic and bootstrap properties of rank regressions

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  • Subbotin, Viktor

Abstract

The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9030.

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Date of creation: 08 Nov 2007
Date of revision: 20 Mar 2008
Handle: RePEc:pra:mprapa:9030

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Keywords: Rank Estimators; Bootstrap; M-Estimators; U-Statistics; U-Processes;

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  1. Yoshihiko Nishiyama & Peter M Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," STICERD - Econometrics Paper Series /2005/483, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  3. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  4. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  5. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
  6. Jason Abrevaya, 1999. "Rank estimation of a transformation model with observed truncation," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 292-305.
  7. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  8. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
  9. Han, Aaron K., 1987. "A non-parametric analysis of transformations," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 191-209, July.
  10. Asparouhova, Elena & Golanski, Robert & Kasprzyk, Krzysztof & Sherman, Robert P. & Asparouhov, Tihomir, 2002. "Rank Estimators For A Transformation Model," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1099-1120, October.
  11. Abrevaya, Jason, 2003. "Pairwise-Difference Rank Estimation of the Transformation Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 437-47, July.
  12. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
  13. Abrevaya, Jason, 1999. "Computation of the maximum rank correlation estimator," Economics Letters, Elsevier, vol. 62(3), pages 279-285, March.
  14. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
  15. Imbens, Guido & Abadie, Alberto, 2008. "On the Failure of the Bootstrap for Matching Estimators," Scholarly Articles 3043415, Harvard University Department of Economics.
  16. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  17. Abrevaya, Jason, 1999. "Leapfrog estimation of a fixed-effects model with unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 93(2), pages 203-228, December.
  18. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  19. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
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Cited by:
  1. Abby Alpert & David Powell, 2012. "Tax Elasticity of Labor Earnings for Older Individuals," Working Papers wp272, University of Michigan, Michigan Retirement Research Center.

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