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Asymptotic distributions of two "synthetic data" estimators for censored single-index models

Listed author(s):
  • Lu, Xuewen
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    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) [1]. 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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 4 (April)
    Pages: 999-1015

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:999-1015
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    1. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March.
    2. 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.
    3. 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.
    4. 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.
    5. G rgens, Tue, 2004. "Average Derivatives For Hazard Functions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 437-463, June.
    6. 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.
    7. Srinivasan, C. & Zhou, M., 1994. "Linear Regression with Censoring," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 179-201, May.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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