Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Simultaneous confidence bands and hypothesis testing for single-index models

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

2015

Source Publication Title

Statistica Sinica

Volume

24

Issue

2

Start Page

937

End Page

955

Publisher

Academia Sinica, Institute of Statistical Science

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

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