Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

$48.00 plus tax (Refund Policy)

Download / Buy Article:

Abstract:

Summary. 

In this article, we propose a new generalized index to recover relationships between two sets of random vectors by finding the vector projections that minimize an L 2 distance between each projected vector and an unknown function of the other. The unknown functions are estimated using the Nadaraya–Watson smoother. Extensions to multiple sets and groups of multiple sets are also discussed, and a bootstrap procedure is developed to detect the number of significant relationships. All the proposed methods are assessed through extensive simulations and real data analyses. In particular, for environmental data from Los Angeles County, we apply our multiple-set methodology to study relationships between mortality, weather, and pollutants vectors. Here, we detect existence of both linear and nonlinear relationships between the dimension-reduced vectors, which are then used to build nonlinear time-series regression models for the dimension-reduced mortality vector. These findings also illustrate potential use of our method in many other applications. A comprehensive assessment of our methodologies along with their theoretical properties are given in a Web Appendix.

Keywords: Bootstrapping; Dimension reduction; Nadaraya–Watson smoother; Nonlinear time-series regression model; Projection pursuit

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1541-0420.2010.01396.x

Affiliations: 1: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23185, U.S.A. 2: Department of Statistics, University of Georgia, Athens, Georgia 30602, U.S.A.

Publication date: December 1, 2010

Related content

Tools

Favourites

Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more