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

Handle URI:
http://hdl.handle.net/10754/626683
Title:
Composite Estimation for Single-Index Models with Responses Subject to Detection Limits
Authors:
Tang, Yanlin; Wang, Huixia Judy ( 0000-0002-5195-8564 ) ; Liang, Hua
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.
Publisher:
Wiley-Blackwell
Journal:
Scandinavian Journal of Statistics
KAUST Grant Number:
OSR-2015-CRG4-2582
Issue Date:
3-Nov-2017
DOI:
10.1111/sjos.12307
Type:
Article
ISSN:
0303-6898
Sponsors:
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).
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Full metadata record

DC FieldValue Language
dc.contributor.authorTang, Yanlinen
dc.contributor.authorWang, Huixia Judyen
dc.contributor.authorLiang, Huaen
dc.date.accessioned2018-01-04T07:51:39Z-
dc.date.available2018-01-04T07:51:39Z-
dc.date.issued2017-11-03en
dc.identifier.citationTang 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.en
dc.identifier.issn0303-6898en
dc.identifier.doi10.1111/sjos.12307en
dc.identifier.urihttp://hdl.handle.net/10754/626683-
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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).en
dc.publisherWiley-Blackwellen
dc.titleComposite Estimation for Single-Index Models with Responses Subject to Detection Limitsen
dc.typeArticleen
dc.identifier.journalScandinavian Journal of Statisticsen
dc.contributor.institutionSchool of Mathematical Sciences; Tongji Universityen
dc.contributor.institutionDepartment of Statistics; The George Washington Universityen
kaust.grant.numberOSR-2015-CRG4-2582en
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