The bootstrap and the Edgeworth correction for semiparametric averaged derivatives
In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of interest, especially in sample sizes that are not enormous. We show that a bootstrap distribution achieves a valid Edgeworth correction in case of density-weighted averaged derivative estimates of semiparametric index models. Approaches to bias-reduction are discussed. We also develop a higher order expansion, to show that the bootstrap achieves a further reduction in size distortion in case of two-sided testing. The finite sample performance of the methods is investigated by means of Monte Carlo simulations froma Tobit model.
|Date of creation:||01 Oct 2004|
|Date of revision:|
|Contact details of provider:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
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.:
- Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
- P. M. Robinson, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 511-534.
- Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
- Joel L. Horowitz, 1996.
"Bootstrap Methods for Median Regression Models,"
- Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
- Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-80, May.
- Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
- Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
- Hardle, W. & Hart, J. & Marron, J. & Tsybakov, A., 1991.
"Bandwidth choice for average derivative estimation,"
CORE Discussion Papers
1991049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- HÄRDLE, Wolfgang & HART, Jeffrey & MARRON, Steve & TSYBAKOV, Alexander, . "Bandwith choice for average derivative estimation," CORE Discussion Papers RP 977, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Haerdle,W. & Hart,J.D. & Marron,J.S. & Tsybakov,A.B., 1989. "Bandwidth choice for average derivative estimation," Discussion Paper Serie A 200, University of Bonn, Germany.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
- 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.
- Arcones, Miguel A. & Giné, Evarist, 1994. "U-processes indexed by Vapnik-Cervonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 17-38, August.
- Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:12/04. 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: (Emma Hyman)
If references are entirely missing, you can add them using this form.