A multiple-index model and dimension reduction

Journal of the American Statistical Association

Volumn 103, Issue 484, 2008, Pages 1631-1640

  Xia, Yingcun ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Asymptotic distribution; Convergence of algorithm; Dimension reduction; Local linear smoother; Semiparametric model.

Indexed keywords

EID: 78649574232     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214508000000805     Document Type: Article

References (36)

1. Banerjee, A. N. (2007), "A Method of Estimating the Average Derivative," Journal of Econometrics, 136, 65-88.
2. Carroll, R. J., Fan, J., Gijbels, I., and Wand, M. P. (1997), "Generalized Partially Linear Single-Index Models," Journal of the American Statistical Association, 92, 477-489.
3. Cook, R. D. (1998), Regression Graphics, New York: Wiley.
4. Cook, R. D., and Li, B. (2002), "Dimension Reduction for Conditional Mean in Regression," The Annals of Statistics, 30, 455-474.
5. Delecroix, M., Hristache, M., and Patilea, V. (2005), "On Semiparametric MEstimation in Single-Index Regression," Journal of Statistical Planning and Inference, 136, 730-769.
6. Donkers, B., and Schafgans, M. M. A. (2003), "A Derivative Based Estimator for Semiparametric Index Models," CentER Discussion Paper 22, Tilburg University.
7. Fan, J., and Gijbels, I. (1996), Local Polynomial Modeling and Its Applications, London: Chapman & Hall.
8. Fan, J., and Huang, T. (2005), "Profile Likelihood Inferences on Semiparametric Varying-Coefficient Partially Linear Models," Bernoulli, 11, 1031-1057.
9. Gao, J., and Tong, H. (2004), "Semiparametric Nonlinear Time Series Model Selection," Journal of the Royal Statistical Society, Ser. B, 66, 321-336.
10. Grenfell, B. T., Finkenstädt, B. F., Wilson, K., Coulson, T. N., and Crawley, M. J. (2000), "Ecology-Nonlinearity and the Moran Effect," Nature, 406, 847.
11. Härdle, W., and Stoker, T. M. (1989), "Investigating Smooth Multiple Regression by Method of Average Derivatives," Journal of the American Statistical Association, 84, 986-995.
12. Härdle, W., Hall, P., and Ichimura, H. (1993), "Optimal Smoothing in Single- Index Models," The Annals of Statistics, 21, 157-178.
13. Horowitz, J. (1998), Semiparametric Methods in Econometrics, New York: Springer.
14. Hristache, M., Juditski, A., Polzehl, J., and Spokoiny, V. (2001), "Structure Adaptive Approach for Dimension Reduction," The Annals of Statistics, 29, 1537-1566.
15. Ichimura, H. (1993), "Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models," Journal of Econometrics, 58, 71-120.
16. Ichimura, H., and Lee, L. F. (1991), "Semiparametric Least Squares Estimation of Multiple Index Models: Single Equation Estimation," in Nonparametric and Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium in Economic Theory and Econometrics, eds. W. A. Barnett, J. Powell, and G. Tauchen, Cambridge, U.K.: Cambridge University Press.
17. Li, K. C. (1991), "Sliced Inverse Regression for Dimension Reduction," Journal of the American Statistical Association, 86, 316-342.
18. - (1992), "On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma," Journal of the American Statistical Association, 87, 1025-1039.
19. Maestri, R., et al. (2005), "Linear and Non-Linear Indices of Heart Rate Variability in Chronic Heart Failure: Mutual Interrelationships and Prognostic Value," Computers in Cardiology, 3, 981-984.
20. Newey, W. K., and Stoker, T. M. (1993), "Efficiency of Weighted Average Derivative Estimation and Index Models," Econometrica, 61, 1199-1223.
21. Rao, C. R., and Mitra, S. K. (1971), Generalized Inverse of Matrices and Its Applications, New York: Wiley.
22. Samarov, A. M. (1993), "Exploring Regression Structure Using Nonparametric Functional Estimation," Journal of the American Statistical Association, 88, 836-847.
23. Samarov, A., Spokoiny, V., and Vial, C. (2005), "Component Identification and Estimation in Nonlinear High-Dimensional Regression Models by Structure Adaptation," Journal of the American Statistical Association, 100, 429-445.
24. Scott, D. W. (1992), Multivariate Density Estimation: Theory, Practice and Visualization, New York: Wiley.
25. Sliverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.
26. Speckman, P. (1988), "Kernel Smoothing in Partially Linear Models," Journal of the Royal Statistical Society, Ser. B, 50, 413-436.
27. Tong, H. (1990), Non-Linear Time Series: A Dynamical System Approach, New York: Oxford University Press.
28. Wang, Q. (2003), "Dimension Reduction in Partly Linear Error-in-Response Models With Validation Data," Journal of Multivariate Analysis, 85, 234-252.
29. World Health Organization (2003), report of a WHO/HEI working group, Bonn, Germany. Available at www.euro.who.int/document/e78992.pdf.
30. Xia, Y. (2006), "Asymptotic Distributions of Two Estimators of the Single- Index Model," Econometric Theory, 22, 1112-1137.
31. - (2007), "A Constructive Approach to the Estimation of Dimension Reduction Directions," The Annals of Statistics, 35, 2654-2690.
32. Xia, Y., Tong, H., Li, W. K., and Zhu, L. (2002), "An Adaptive Estimation of Dimension Reduction Space," Journal of the Royal Statistical Society, Ser. B, 64, 363-410.
33. Yang, L., and Tschernig, R. (1999), "Multivariate Bandwidth Selection for Local Linear Regression," Journal of the Royal Statistical Society, Ser. B, 61, 793-815.
34. Yin, X., and Cook, R. D. (2002), "Dimension Reduction for the Conditional k-th Moment in Regression", Journal of the Royal Statistical Society, Ser. B, 64, 159-175.
35. - (2004), "Asymptotic Distribution of Test Statistic for the Covariance Dimension ReductionMethods in Regression," Statistics and Probability Letters, 68, 421-427.
36. Yu, Y., and Ruppert, D. (2002), "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, 97, 1042-1054.