A short note on fitting a single-index model with massive data

Figures & data

Table 1. The means of Absolute Bias, MSE (standard deviation) and t for simulation Example 1.

M	Methods	Absolute bias of ${\hat{\mathit{\gamma }}}_1$	Absolute bias of ${\hat{\mathit{\gamma }}}_2$	MSE	t
1	Oracle	0.0051 (0.0031)	0.0032 (0.0027)	0.0065 (0.0034)	1801
10	ADC	0.0053 (0.0036)	0.0033 (0.0023)	0.0067 (0.0035)	199
	IDC	0.0057 (0.0039)	0.0045 (0.0037)	0.0078 (0.0045)	156
50	ADC	0.0060 (0.0044)	0.0039 (0.0049)	0.0077 (0.0059)	76
	IDC	0.0066 (0.0044)	0.0050 (0.0037)	0.0089 (0.0048)	137
100	ADC	0.0150 (0.0161)	0.0207 (0.0931)	0.0204 (0.0227)	95
	IDC	0.0122 (0.0133)	0.0103 (0.0515)	0.0126 (0.0143)	132

Figure 1. Comparison of MSE versus the number of blocks M with $\tilde{n}=100$ for three methods for simulation Example 3.2.

Figure 2. The mean computing time of $\hat{\mathit{\gamma }}$ (in seconds) for simulation Example 3.2.

Table 2. The means of Absolute Bias (standard deviation) and t for simulation Example 3.

		n = 5000		n = 10000		n = 20000
M	Methods	Absolute bias	t	Absolute bias	t	Absolute bias	t
1	Oracle	0.0083 (0.0042)	174	0.0048 (0.0036)	699	0.0043 (0.0032)	2628
10	ADC	0.0113 (0.0099)	22	0.0085 (0.0058)	76	0.0047 (0.0038)	287
	IDC	0.0239 (0.0015)	40	0.0118 (0.0090)	152	0.0051 (0.0044)	591
50	ADC	0.0731 (0.0571)	20	0.0140 (0.0092)	32	0.0051 (0.0027)	78
	IDC	0.0404 (0.0407)	53	0.0128 (0.0097)	178	0.0047 (0.0051)	640
100	ADC	0.1358 (0.0496)	34	0.0565 (0.0467)	41	0.0057 (0.0065)	62
	IDC	0.0893 (0.0293)	106	0.0347 (0.0259)	215	0.0051 (0.0060)	696

Figure 3. Estimated single index function for the combined cycle power plant data. The dots are the observations EP and the curve is the estimated EP by the Oracle method.

Table 3. The coefficient estimates and MSFE for the combined cycle power plant data.

M	Method	AT	AP	RH	V	MSFE	t
1	Oracle	1.0000	−0.0290	0.1326	0.2572	0.0627	4864
8	ADC	1.0000	−0.0287	0.1306	0.2670	0.0627	695
	IDC	1.0000	−0.0401	0.1348	0.2624	0.0628	229
16	ADC	1.0000	−0.0284	0.1299	0.2717	0.0627	395
	IDC	1.0000	−0.0346	0.1282	0.2657	0.0628	157
26	ADC	1.0000	−0.0267	0.1297	0.2727	0.0627	271
	IDC	1.0000	−0.0346	0.1282	0.2659	0.0628	154
46	ADC	1.0000	−0.0336	0.1256	0.2665	0.0628	222
	IDC	1.0000	−0.0345	0.1283	0.2654	0.0628	149
92	ADC	1.0000	−0.0391	0.1271	0.2702	0.0633	219
	IDC	1.0000	−0.0353	0.1275	0.2694	0.0628	145

Table 4. The coefficient estimates and MAPE for the airline on-time data.

Method	HD	DIS	NF	WF	MAPE
LS	0.0044	−0.0505	−0.0004	−0.0451	0.2179
ADC	1.0000	−0.0271	0.0256	−0.0030	0.2051
IDC	1.0000	−0.0106	0.1216	−0.6948	0.2014