Composite Estimation for Single-Index Models with Responses Subject to Detection Limits

Tang, Yanlin; Wang, Huixia Judy; Liang, Hua

Composite Estimation for Single-Index Models with Responses Subject to Detection Limits

Type

Article

Authors

Tang, Yanlin
Wang, Huixia Judy

Liang, Hua

KAUST Grant Number

OSR-2015-CRG4-2582

Date

2017-11-03

Abstract

We propose a semiparametric estimator for single-index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non-parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy-tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.

Citation

Tang Y, Wang HJ, Liang H (2017) Composite Estimation for Single-Index Models with Responses Subject to Detection Limits. Scandinavian Journal of Statistics. Available: http://dx.doi.org/10.1111/sjos.12307.

Acknowledgements

The authors would like to thank two anonymous reviewers, an associate editor and the editor for constructive comments and helpful suggestions. This research was partially supported by National Natural Science Foundation of China (NSFC) grants 11301391 and 11526133 (Tang), NSFC grant 11529101 (Liang), National Science Foundation (NSF) grant DMS-1418042 (Liang), NSF CAREER AwardDMS-1149355 (Wang) and the OSR-2015-CRG4-2582 grant from KAUST (Wang and Tang).