Optimal Smoothing for a Computationally and Statistically Efficient Single Index Estimator
In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result as we show from inefficient estimation methods or technical difficulties. Based on local linear kernel smoother, we propose an estimation method to estimate the single-index model without under-smoothing. Under some conditions, our estimator of the single-index is asymptotically normal and most efficient in the semi-parametric sense. Moreover, we derive higher expansions for our estimator and use them to define an optimal bandwidth for the purposes of index estimation. As a result we obtain a practically more relevant method and we show its superior performance in a variety of applications.
|Date of creation:||May 2009|
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- Y. Nishiyama & Peter Robinson, 2004.
"The bootstrap and the Edgeworth correction for semiparametric averaged derivatives,"
CeMMAP working papers
CWP12/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, 05.
- 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.
- Hardle, W. & Tsybakov, A., 1991.
"How sensitive are average derivates ?,"
CORE Discussion Papers
1991044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
- 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.
- Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," CORE Discussion Papers 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
- Oliver Linton, 1993.
"Second Order Approximation in the Partially Linear Regression Model,"
Cowles Foundation Discussion Papers
1065, Cowles Foundation for Research in Economics, Yale University.
- Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
- Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1112-1137, December.
- repec:cup:cbooks:9780521424318 is not listed on IDEAS
- Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
- Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The bootstrap and the Edgeworth correction for semiparametric averaged derivatives," LSE Research Online Documents on Economics 2297, London School of Economics and Political Science, LSE Library.
- repec:cup:cbooks:9780521370905 is not listed on IDEAS
- Xiangrong Yin & R. Dennis Cook, 2005. "Direction estimation in single-index regressions," Biometrika, Biometrika Trust, vol. 92(2), pages 371-384, June.
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