Table 3.

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), 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, and the usual F-test for different settings with n = 200 and M = 10. 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.

	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(·)	F-test	0.050	0.325	0.940	1.000	1.000	0.052	0.302	0.900	0.998	1.000	0.058	0.183	0.694	0.966	1.000
	KInt	0.054	0.371	0.953	1.000	1.000	0.052	0.355	0.935	0.999	1.000	0.052	0.170	0.646	0.961	0.999
	KGauss	0.052	0.706	1.000	1.000	1.000	0.051	0.668	0.998	1.000	1.000	0.051	0.487	0.948	1.000	1.000
	KGauss,PCA1	0.049	0.716	0.996	1.000	1.000	0.049	0.644	0.996	1.000	1.000	0.048	0.453	0.953	0.999	1.000
	KGauss,PCA2	0.049	0.721	0.999	1.000	1.000	0.049	0.654	0.995	1.000	1.000	0.048	0.477	0.963	1.000	1.000
	Score test	0.051	0.799	1.000	1.000	1.000	0.055	0.756	0.998	1.000	1.000	0.049	0.644	0.990	1.000	1.000
h2(·)	F-test	0.050	0.476	0.990	1.000	1.000	0.052	0.587	0.998	1.000	1.000	0.058	0.589	0.997	1.000	1.000
	KInt	0.054	0.494	0.986	1.000	1.000	0.052	0.829	1.000	1.000	1.000	0.052	0.893	1.000	1.000	1.000
	KGauss	0.052	0.715	1.000	1.000	1.000	0.051	0.701	0.999	1.000	1.000	0.051	0.611	0.988	1.000	1.000
	KGauss,PCA1	0.049	0.730	0.997	1.000	1.000	0.049	0.744	0.997	1.000	1.000	0.048	0.719	0.998	1.000	1.000
	KGauss,PCA2	0.049	0.737	0.996	1.000	1.000	0.049	0.774	0.999	1.000	1.000	0.048	0.709	0.999	1.000	1.000
	Score test	0.051	0.884	0.999	1.000	1.000	0.055	0.992	1.000	1.000	1.000	0.049	1.000	1.000	1.000	1.000
h3(·)	F-test	0.043	0.112	0.414	0.817	0.956	0.044	0.070	0.176	0.419	0.713	0.054	0.065	0.102	0.196	0.305
	KInt	0.044	0.117	0.435	0.837	0.964	0.045	0.094	0.274	0.572	0.841	0.044	0.064	0.099	0.216	0.326
	KGauss	0.049	0.274	0.828	0.989	1.000	0.051	0.253	0.690	0.922	0.987	0.052	0.168	0.443	0.715	0.894
	KGauss,PCA1	0.046	0.293	0.803	0.981	0.999	0.051	0.234	0.641	0.912	0.986	0.051	0.153	0.439	0.712	0.866
	KGauss,PCA2	0.046	0.295	0.819	0.983	0.999	0.051	0.244	0.652	0.914	0.984	0.051	0.171	0.459	0.721	0.881
h4(·)	F-test	0.043	0.091	0.301	0.678	0.944	0.044	0.065	0.168	0.421	0.725	0.054	0.063	0.120	0.207	0.380
	KInt	0.044	0.090	0.328	0.696	0.957	0.045	0.098	0.336	0.661	0.895	0.044	0.089	0.214	0.435	0.676
	KGauss	0.049	0.190	0.700	0.963	0.996	0.051	0.201	0.560	0.857	0.970	0.052	0.133	0.349	0.634	0.835
	KGauss,PCA1	0.046	0.226	0.691	0.964	0.996	0.051	0.177	0.524	0.848	0.972	0.051	0.128	0.331	0.619	0.844
	KGauss,PCA2	0.042	0.215	0.690	0.963	0.996	0.053	0.174	0.534	0.853	0.977	0.051	0.124	0.342	0.606	0.889