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 the 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 the case of two-sided testing. The finite-sample performance of the methods is investigated by means of Monte Carlo simulations from a Tobit model. Copyright The Econometric Society 2005.
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Volume (Year): 73 (2005)
Issue (Month): 3 (05)
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- Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
- Joel L. Horowitz, 1998.
"Bootstrap Methods for Median Regression Models,"
Econometric Society, vol. 66(6), pages 1327-1352, November.
- Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
- Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
- 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.
- 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.
- 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.
- HÄRDLE, Wolfgang & HART, Jeffrey & MARRON, Steve & TSYBAKOV, Alexander, "undated".
"Bandwith choice for average derivative estimation,"
CORE Discussion Papers RP
977, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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).
- 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.
- Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
- 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.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
- Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-680, May.
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