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A semiparametric approach to canonical analysis
Author(s) -
Xia Yingcun
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00647.x
Subject(s) - canonical correlation , canonical correspondence analysis , canonical analysis , semiparametric regression , non canonical , mathematics , canonical form , set (abstract data type) , semiparametric model , computer science , econometrics , statistics , regression analysis , nonparametric statistics , pure mathematics , ecology , abundance (ecology) , biology , programming language , microbiology and biotechnology
Summary. Classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables. We propose a method, called semiparametric canonical analysis, to generalize canonical correlation analysis to incorporate the important non‐linear association. Semiparametric canonical analysis is easy to implement and interpret. Statistical properties are proved. A consistent estimation method is developed. Selection of significant semiparametric canonical analysis components is discussed. Simulations suggest that the methods proposed have satisfactory performance in finite samples. One environmental data set and one data set in social science are investigated, in which non‐linear canonical associations are observed and interpreted.