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Statistica Sinica 30 (2020), 829-843

ESTIMATION OF SINGLE-INDEX MODELS WITH
FIXED CENSORED RESPONSES
Hailin Huang1 , Yuanzhang Li1 , Hua Liang1 and Yanlin Tang2
1George Washington University and 2East China Normal University

Abstract: We propose a new procedure to estimate the index parameter and link function of single-index models, where the response variable is subject to fixed censoring. Under some regularity conditions, we show that the estimated index parameter is root-n consistent and asymptotically normal, and the estimated nonparametric link function achieves the optimal convergence rate and is asymptotically normal. In addition, we propose a linearity testing method for the nonparametric link function. A simulation study shows that the proposed procedures perform well in finite-sample experiments. An application to an HIV data set is presented for illustrative purposes.

Key words and phrases: Nonparametric censored regression, semi-parametric least-squares, single-index model.

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