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

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  • Lu, Xuewen

Abstract

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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  • Lu, Xuewen, 2010. "Asymptotic distributions of two "synthetic data" estimators for censored single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 999-1015, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:999-1015
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    Cited by:

    1. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Semiparametric estimation of fixed effects panel data single-index model," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1595-1602.
    2. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.

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