Estimation and inference in functional single-index models

Shujie Ma ()

Annals of the Institute of Statistical Mathematics, 2016, vol. 68, issue 1, 208 pages

Abstract: We propose a functional single-index model (FSiM) to study the link between a scalar response variable and multiple functional predictors, in which the mean of the response is related to the linear predictors via an unknown link function. The FSiM serves as a good tool for dimension reduction in regression with multiple predictors and it is more flexible than functional linear models. Assuming that the functional predictors are observed at discrete points, we use B-spline basis functions to estimate the slope functions and the link function based on the least-squares criterion, and propose an iterative estimating procedure. Moreover, we provide uniform convergence rates of the proposed spline estimators in the FSiM, and construct asymptotic simultaneous confidence bands for the slope functions for inference. Our proposed method is illustrated by simulation studies and by an analysis of a diffusion tensor imaging data application. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Keywords: Single-index models; Functional data analysis; Functional linear models; B splines; Confidence bands; Simultaneous inference (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10463-014-0488-3 (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:spr:aistmt:v:68:y:2016:i:1:p:181-208

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-014-0488-3

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().