TY - JOUR
T1 - Dependence maps
T2 - Local dependence in practice
AU - Jones, M. C.
AU - Koch, I.
PY - 2003/8/1
Y1 - 2003/8/1
N2 - There is often more structure in the way two random variables are associated than a single scalar dependence measure, such as correlation, can reflect. Local dependence functions such as that of Holland and Wang (1987) are, therefore, useful. However, it can be argued that estimated local dependence functions convey information that is too detailed to be easily interpretable. We seek to remedy this difficulty, and hence make local dependence a more readily interpretable practical tool, by introducing dependence maps. Via local permutation testing, dependence maps simplify the estimated local dependence structure between two variables by identifying regions of (significant) positive, (not significant) zero and (significant) negative local dependence. When viewed in conjunction with an estimate of the joint density, a comprehensive picture of the joint behaviour of the variables is provided. A little theory, many implementational details and several examples are given.
AB - There is often more structure in the way two random variables are associated than a single scalar dependence measure, such as correlation, can reflect. Local dependence functions such as that of Holland and Wang (1987) are, therefore, useful. However, it can be argued that estimated local dependence functions convey information that is too detailed to be easily interpretable. We seek to remedy this difficulty, and hence make local dependence a more readily interpretable practical tool, by introducing dependence maps. Via local permutation testing, dependence maps simplify the estimated local dependence structure between two variables by identifying regions of (significant) positive, (not significant) zero and (significant) negative local dependence. When viewed in conjunction with an estimate of the joint density, a comprehensive picture of the joint behaviour of the variables is provided. A little theory, many implementational details and several examples are given.
KW - Association
KW - Bivariate distribution
KW - Correlation
KW - Kernel smoothing
KW - Permutation test
UR - http://www.scopus.com/inward/record.url?scp=0347093593&partnerID=8YFLogxK
U2 - 10.1023/A:1024270700807
DO - 10.1023/A:1024270700807
M3 - Article
AN - SCOPUS:0347093593
VL - 13
SP - 241
EP - 255
JO - Statistics and Computing
JF - Statistics and Computing
SN - 0960-3174
IS - 3
ER -