Asymptotic distributions of two "synthetic data" estimators for censored single-index models
The censored single-index model provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored and the link function is unknown. It presents a technique for "dimension reduction" in semiparametric censored regression models and generalizes the existing accelerated failure time models for survival analysis. This paper proposes two methods for estimation of single-index models with randomly censored samples. We first transform the censored data into synthetic data or pseudo-responses unbiasedly, then obtain estimates of the index coefficients by the rOPG or rMAVE procedures of Xia (2006) . Finally, we estimate the unknown nonparametric link function using techniques for univariate censored nonparametric regression. The estimators for the index coefficients are shown to be root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodologies.
Volume (Year): 101 (2010)
Issue (Month): 4 (April)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Arthur Lewbel & Oliver Linton, 2002.
"Nonparametric Censored and Truncated Regression,"
Econometric Society, vol. 70(2), pages 765-779, March.
- Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," Econometric Society World Congress 2000 Contributed Papers 1237, Econometric Society.
- Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," Boston College Working Papers in Economics 439, Boston College Department of Economics.
- Arthur Lewbel & Oliver Linton, 2000. "Nonparametric censored and truncated regression," LSE Research Online Documents on Economics 2060, London School of Economics and Political Science, LSE Library.
- Arthur Lewbel & Oliver Linton, 2000. "Nonparametric Censored and Truncated Regression," STICERD - Econometrics Paper Series 389, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Srinivasan, C. & Zhou, M., 1994. "Linear Regression with Censoring," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 179-201, May.
- 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.
- 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.
- Lai, T. L. & Ying, Z. L. & Zheng, Z. K., 1995. "Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 259-279, February.
- Cédric Heuchenne & Ingrid Keilegom, 2007. "Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 273-297, June.
- Lu, Xuewen & Burke, M.D., 2005. "Censored multiple regression by the method of average derivatives," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 182-205, July.
- 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.
- G rgens, Tue, 2004. "Average Derivatives For Hazard Functions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 437-463, June.
- Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
- Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:999-1015. 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: (Dana Niculescu)
If references are entirely missing, you can add them using this form.