Table 3.

Squared bias BSQ, variance VAR and mean-squared error MSE for the data-based simulation of a quadratic variance function described in Section 7.2^†

Estimator	Results for α = 0.2037			Results for β = 0.1779
	BSQ	VAR	MSE	BSQ	VAR	MSE
m = 5
N–R	1.3433	4.4321	5.7754	12.4622	23.1686	35.6308
S–R	65.0631	214.7426	279.8057	11.0667	35.6630	46.7297
PS–R	6.3592	19.3418	25.7011	0.9517	3.4602	4.4119
Semi–2	0.2218	0.8070	1.0288	0.0286	2.2274	2.2559
I–R	0.0037	1.7305	1.7342	0.0023	0.7512	0.7536
m = 10
N–R	0.1874	0.9545	1.1419	2.4045	3.9017	6.3062
S–R	6.1626	9.9917	16.1543	1.0934	2.2355	3.3289
PS–R	0.3231	0.4425	0.7656	0.0555	0.1278	0.1833
Semi–2	0.1008	0.2546	0.3554	0.0759	0.0630	0.1390
I–R	0.0001	0.4850	0.4851	0.0000	0.2314	0.2314
m = 15
N–R	0.0379	0.6179	0.6558	0.8797	2.3901	3.2698
S–R	2.2256	4.7006	6.9262	0.3842	1.1034	1.4876
PS–R	0.0404	0.4312	0.4716	0.0088	0.1575	0.1663
Semi–2	0.0053	0.1214	0.1268	0.0429	0.0457	0.0886
I–R	0.0004	0.3912	0.3916	0.0003	0.1823	0.1827
m = 20
N–R	0.0081	0.3162	0.3243	0.4198	1.0678	1.4876
S–R	1.1577	1.5012	2.6589	0.2022	0.4225	0.6247
PS–R	0.0101	0.2219	0.2320	0.0021	0.1019	0.1040
Semi–2	0.0020	0.1017	0.1037	0.0515	0.0365	0.0880
I–R	0.0000	0.2659	0.2659	0.0000	0.1273	0.1273

^†All quantities are multiplied by 100. The sample size is n = 3051. The symbols ‘N’, ‘S’, ‘PS’ and ‘I’ refer to the naive, SIMEX, permutation SIMEX and ideal estimators respectively, where ideal here means that X is observed. ‘R’ refers to the least square estimators. Semi–2 is the semiparametric estimator partitioned into two groups.