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 -