Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

In this paper, we propose simultaneous confidence bands for the nonparametric link function in single-index models in the presence of a nuisance index parameter. We establish the asymptotic properties for the link function and its derivative that allow simultaneous confidence bands for various inference tasks. In addition, we propose an adaptive Neyman test statistic for testing the linearity of the link function. We then conduct simulation studies to evaluate the performance of the proposed method, and apply them to two data sets for illustration.

Keywords

Adaptive Neyman test, Difference-based estimator, Local linear smoother, Residual variance, Simultaneous confidence band, Single-index model

Publication Date

4-2014

Source Publication Title

Statistica Sinica

Volume

24

Issue

2

Start Page

937

End Page

955

Publisher

Academia Sinica, Institute of Statistical Science

Peer Reviewed

1

Funder

Gaorong Li’s research was supported by the NSFC (11101014, 11201306), the Natural Science Foundation of Beijing (1142002), the Science and Technology Project of Beijing Municipal Education Commission (KM201410005010), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20101103120016), PHR(IHLB, PHR20110822) and Program for JingHua Talents in Beijing University of Technology. Heng Peng’s research was supported by CERG grants from the Hong Kong Research Grants Council (HKBU 201610, HKBU 201809 and HKBU 202012), FRG grants from Hong Kong Baptist University (FRG2/11-12/130 and FRG2/12-13/077, and a grant from the NSFC (11271094). Tiejun Tong’s research was supported by Hong Kong RGC grant HKBU 202711.

DOI

10.5705/ss.2012.127

Link to Publisher's Edition

http://dx.doi.org/10.5705/ss.2012.127

ISSN (print)

10170405

ISSN (electronic)

19968507

Included in

Mathematics Commons

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