The bootstrap and the edgeworth correction for semiparametric averaged derivatives

Econometrica

Volumn 73, Issue 3, 2005, Pages 903-948

  Nishiyama, Yoshihiko ^a   Robinson, Peter M ^b  

^a KYOTO UNIVERSITY   (Japan)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Bootstrap; Edgeworth correction; Semiparametric averaged derivatives

Indexed keywords

EID: 27744577028     PISSN: 00129682     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1468-0262.2005.00598.x     Document Type: Article

References (26)

1. BICKEL, P. J., AND D. A. FREEDMAN (1981): "Some Asymptotic Theory for the Bootstrap," The Annals of Statistics, 9, 1196-1217.
2. BICKEL, P. J., F. GÖTZE, AND W. R. VAN ZWET (1986): "The Edgeworth Expansion for U-Statistics of Degree Two," The Annals of Statistics, 14, 1463-1484.
3. CHUNG, K. L. (1974) :A Course in Probability Theory. New York: Academic Press.
4. DHARMARDHIKARI, S. W., V. FABIAN, AND K. JOGDEO (1968): "Bounds on the Moments of Martingales," The Annals of Mathematical Statistics, 39, 1719-1723.
5. EFRON, B. (1979): "Bootstrap Methods: Another Look at the Jackknife," The Annals of Statistics, 7, 1-26.
6. FREEDMAN, D. A. (1981): "Bootstrapping Regression Models," The Annals of Statistics, 9, 1218-1228.
7. _ (1984): "Bootstrapping Two-Stage Least-Squares Estimates in Stationary Linear Models," The Annals of Statistics, 12, 827-842.
8. HALL, P. (1986): "On the Bootstrap of Confidence Intervals," The Annals of Statistics, 14, 1431-1452.
9. _ (1991): "Edgeworth Expansions for Nonparametric Density Estimators, with Applications," Statistics, 22, 215-232.
10. _ (1992): The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag.
11. HÅRDLE, W., J. HART, J. S. MARRON, AND A. B. TSYBAKOV (1992): "Bandwidth Choice for Average Derivative Estimation," Journal of the American Statistical Association, 84, 218-226.
12. HELMERS, R. (1991): "On the Edgeworth Expansion and the Bootstrap Approximation for a Studentized U-Statistic," The Annals of Statistics, 19, 470-484.
13. HOROWITZ, J. L. (1992): "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, 60, 505-531.
14. _ (1997): "Bootstrap Methods in Econometrics: Theory and Numerical Performance," in Advances in Economics and Econometrics, ed. by D. M. Kreps and K. F. Wallis. New York: Cambridge University Press, 188-222.
15. _ (1998): "Bootstrap Methods for Median Regression Models," Econometrica, 66, 1327-1351.
16. _ (2002): "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Journal of Econometrics, 111, 141-167.
17. MAESONO, C. F. (1997): "Edgeworth Expansion of a Studentized U-Statistic and a Jackknife Estimator of Variance," Journal of Statistical Planning and Inference, 61, 61-84.
18. MANSKI, C. F. (1985): "Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator," Journal of Econometrics, 32, 65-108.
19. NISHIYAMA, Y., AND P. M. ROBINSON (2000): "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, 68, 931-980.
20. _ (2001): "Studentization in Edgeworth Expansions for Estimates of Semiparametric Single Index Models," in Nonlinear Statistical Modeling (Festschrift for Takeshi Amemiya), ed. by C. Hsiao, K. Morimune, and J. Powell. Cambridge, U.K.: Cambridge University Press, 197-240.
21. POWELL, J. L., J. H. STOCK, AND T. M. STOKER (1989): "Semiparametric Estimation of Index Coefficients," Econometrica, 57, 1403-1430.
22. POWELL, J. L., AND T. M. STOKER (1996): "Optimal Bandwidth Choice for Density-Weighted Averages," Journal of Econometrics, 75, 291-316.
23. QUMSIYEH, M. (1986): "Edgeworth Expansions in Regression and Comparison of Edgeworth Expansion and Bootstrap Methodologies," Unpublished Ph.D. Dissertation, Indiana University.
24. ROBINSON, P. M. (1988): "Root-N-Consistent Semiparametric Regression," Econometrica, 56, 931-954.
25. _ (1989): "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," Review of Economic Studies, 56, 511-534.
26. _ (1995): "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, 63, 667-680.