Empirical likelihood confidence regions in the single-index model with growing dimensions
Guangren Yang,
Xia Cui and
Sumin Hou
Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 15, 7562-7579
Abstract:
This paper investigates statistical inference for the single-index model when the number of predictors grows with sample size. Empirical likelihood method for constructing confidence region for the index vector, which does not require a multivariate non parametric smoothing, is employed. However, the classical empirical likelihood ratio for this model does not remain valid because plug-in estimation of an infinite-dimensional nuisance parameter causes a non negligible bias and the diverging number of parameters/predictors makes the limit not chi-squared any more. To solve these problems, we define an empirical likelihood ratio based on newly proposed weighted estimating equations and show that it is asymptotically normal. Also we find that different weights used in the weighted residuals require, for asymptotic normality, different diverging rate of the number of predictors. However, the rate n1/3, which is a possible fastest rate when there are no any other conditions assumed in the setting under study, is still attainable. A simulation study is carried out to assess the performance of our method.
Date: 2017
References: Add references at CitEc
Citations:
Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2016.1157190 (text/html)
Access to full text is restricted to subscribers.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:46:y:2017:i:15:p:7562-7579
Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20
DOI: 10.1080/03610926.2016.1157190
Access Statistics for this article
Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe
More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().