. Author manuscript; available in PMC: 2014 Feb 1.

Published in final edited form as: Ann Inst Stat Math. 2013 Jun 16;66(1):1–31. doi: 10.1007/s10463-013-0415-z

Table 1.

Simulation results under homoscedastic residuals (Cases (i) and (ii))

n=40	MSPE	cov(y)^a	Case (i) MISE	cov(η)^b	L	MSPE	cov(y)	Case (ii) MISE	cov(η)	L
P1	0.2997	1	0.0248	1	0.0017	0.6043	1	0.0232	1	0.0027
P2a	0.2821	0.9980	0.0141	1	0.0015	0.5983	0.9740	0.0173	1	0.0019
P2b	0.2798	1	0.0144	1	0.0015	0.5987	0.9745	0.0169	1	0.0017
P2c	0.2980	1	0.0156	1	0.0016	0.5980	0.9750	0.0189	1	0.0020
P2d	0.2869	1	0.0155	1	0.0016	0.5983	0.9750	0.0190	1	0.0020
M-Estimation	0.2820		0.0140			0.6013		0.0177
BART	0.3510	0.6866	0.0714			0.7051	0.7845	0.0950
Treed GP	0.3042	0.9134	0.0256			0.6968	0.9365	0.0803

n=60	MSPE	cov(y)	MISE	cov(η)	L	MSPE	cov(y)	MISE	cov(η)	L

P1	0.2990	1	0.0246	1	0.0019	0.5776	1	0.0242	1	0.0023
P2a	0.2769	0.9947	0.0103	1	0.0017	0.5471	0.95	0.0143	0.97	0.0016
P2b	0.2752	0.9963	0.0104	1	0.0016	0.5541	0.95	0.0141	0.98	0.0016
P2c	0.2852	0.9945	0.0176	1	0.0019	0.5664	0.95	0.0142	0.99	0.0021
P2d	0.2826	0.9960	0.0173	1	0.0018	0.5561	0.95	0.0141	0.98	0.0021
M-Estimation	0.2759		0.0103			0.5623		0.0139
BART	0.3314	0.6753	0.0539			0.6725	0.7777	0.1098
Treed GP	0.3000	0.9193	0.0218			0.6880	0.9301	0.1198

n=80	MSPE	cov(y)	MISE	cov(η)	L	MSPE	cov(y)	MISE	cov(η)	L

P1	0.2913	1	0.0252	1	0.0021	0.5583	1	0.0172	1	0.0022
P2a	0.2592	0.9940	0.0086	1	0.0021	0.4989	0.97	0.0050	1	0.0014
P2b	0.2574	0.9956	0.0069	1	0.0020	0.4898	0.98	0.0067	1	0.0010
P2c	0.2724	0.9976	0.0187	1	0.0020	0.5104	0.98	0.0103	1	0.0017
P2d	0.2716	0.9976	0.0189	1	0.0020	0.5002	0.98	0.0097	1	0.0018
M-Estimation	0.2720		0.0079			0.5431		0.0068
BART	0.3128	0.6525	0.0437			0.6509	0.7815	0.1098
Treed GP	0.2886	0.9301	0.0175			0.6532	0.9224	0.1031

cov(y) denotes the coverage of the 95% predictive intervals of the test cases

cov(η) denotes the coverage of the 95% credible intervals of the mean regression function