Table 4.

Results of the simulation study described in Section 5. Displayed are the empirical size (c = 0) and power (c = 2,…, 8) of the proposed garrote kernel machine (GKM) test using the two-way interaction kernel (K_Int), the Gaussian kernel (K_Gauss), and the PCA based test statistics $T_n^{\ast }$ and $T_n^{\ast \ast }$ (K_Gauss,PCA1 and K_Gauss,PCA2) using the Gaussian kernel as in Section 3.3 for different settings with n = 200 and M = 20. Also presented, for the linear cases (h₁(·) and h₂(·)), are the results for the ideal classical score tests assuming the direction of the alternative is known. The nominal level was set be α = 0.05. Note that in this case, F-test is not computable.

	Test	r = 0.0					r = 0.2					r = 0.5
		c = 0	c = 2	c = 4	c = 6	c = 8	c = 0	c = 2	c = 4	c = 6	c = 8	c = 0	c = 2	c = 4	c = 6	c = 8
h1(·)	KInt	0.047	0.068	0.147	0.253	0.436	0.039	0.060	0.123	0.217	0.361	0.049	0.060	0.103	0.193	0.310
	KGauss	0.055	0.578	0.988	1.000	1.000	0.055	0.456	0.948	0.999	1.000	0.051	0.348	0.821	0.988	0.999
	KGauss,PCA1	0.055	0.558	0.982	1.000	1.000	0.053	0.425	0.925	1.000	1.000	0.051	0.286	0.779	0.983	0.998
	KGauss,PCA2	0.055	0.578	0.987	1.000	1.000	0.052	0.448	0.937	1.000	1.000	0.049	0.314	0.811	0.985	0.999
	Score test	0.055	0.768	1.000	1.000	1.000	0.053	0.712	0.996	1.000	1.000	0.052	0.607	0.978	1.000	1.000
h2(·)	KInt	0.047	0.120	0.376	0.670	0.847	0.039	0.812	1.000	1.000	1.000	0.049	1.000	1.000	1.000	1.000
	KGauss	0.055	0.582	0.967	0.999	1.000	0.055	0.942	1.000	1.000	1.000	0.051	0.998	1.000	1.000	1.000
	KGauss,PCA1	0.055	0.578	0.963	0.999	1.000	0.053	0.969	1.000	1.000	1.000	0.051	0.999	1.000	1.000	1.000
	KGauss,PCA2	0.055	0.578	0.967	1.000	1.000	0.052	0.967	1.000	1.000	1.000	0.049	0.999	1.000	1.000	1.000
	Score test	0.055	0.827	0.992	0.999	1.000	0.053	0.996	1.000	1.000	1.000	0.052	1.000	1.000	1.000	1.000
h3(·)	KInt	0.038	0.051	0.07	0.090	0.133	0.050	0.045	0.045	0.047	0.051	0.047	0.045	0.057	0.067	0.087
	KGauss	0.055	0.192	0.594	0.896	0.987	0.054	0.193	0.435	0.695	0.912	0.055	0.127	0.272	0.443	0.623
	KGauss,PCA1	0.055	0.188	0.581	0.889	0.986	0.054	0.169	0.379	0.644	0.857	0.055	0.099	0.198	0.372	0.540
	KGauss,PCA2	0.055	0.194	0.604	0.901	0.987	0.054	0.184	0.414	0.672	0.894	0.055	0.106	0.239	0.407	0.600
h4(·)	KInt	0.038	0.044	0.173	0.217	0.312	0.05	0.077	0.104	0.153	0.242	0.047	0.060	0.106	0.138	0.153
	KGauss	0.055	0.112	0.375	0.784	0.946	0.054	0.153	0.438	0.880	0.994	0.055	0.152	0.529	0.955	1.000
	KGauss,PCA1	0.055	0.110	0.383	0.782	0.946	0.054	0.105	0.396	0.708	0.905	0.055	0.109	0.323	0.697	0.889
	KGauss,PCA2	0.055	0.110	0.391	0.798	0.952	0.054	0.150	0.390	0.811	0.906	0.055	0.114	0.311	0.694	0.919