Efficient test for nonlinear dependence of two continuous variables

BMC Bioinformatics

Table 1 Simulation power in nine simple functions

N = 50, x ~ U(−1,1)	CANOVA2	CANOVA4	CANOVA8	CANOVA12	Pearson	Kendall	Spearman	Distance	Hoeffding	MIC
y = 0 + N(0,1)	0.051	0.048	0.048	0.050	0.047	0.048	0.049	0.039	0.059	0.051
y = x + N(0,1)	0.564	0.798	0.889	0.902	0.972	0.962	0.961	0.950	0.953	0.591
y = 0.5;*(x + 1)² + N(0,1)	0.606	0.836	0.904	0.918	0.968	0.953	0.962	0.964	0.953	0.633
y = sin(Pi*x) + N(0,1)	0.758	0.941	0.966	0.962	0.936	0.918	0.930	0.969	0.969	0.829
y = sin(2Pix) + N(0,1)	0.713	0.886	0.812	0.294	0.318	0.328	0.320	0.341	0.405	0.579
y = sin(3Pix) + N(0,1)	0.677	0.796	0.254	0.076	0.178	0.192	0.199	0.186	0.219	0.423
y = cos(Pi*x) + N(0,1)	0.784	0.940	0.973	0.942	0.067	0.076	0.083	0.660	0.710	0.660
y = cos(2Pix) + N(0,1)	0.738	0.891	0.754	0.142	0.045	0.054	0.053	0.100	0.129	0.548
y = cos(3Pix) + N(0,1)	0.673	0.751	0.160	0.031	0.053	0.054	0.057	0.074	0.090	0.371

ISSN: 1471-2105