Table 1.

Bias(×10) and variance(×10²) of the least squares recursion and the logit-MLE with m = 3, n = 15, and the fully sequentially logit-MLE(f), i.e., m = 1, n = 45. The mean squared error ratio (rmse) is calculated relative to the method assuming known σ.

p	θ	Method assumes	X1 = 0.25, b = β†			X1 = 0.25, b = 0.5β‡			X1 = 0.50, b = β†			X1 = 0.50, b = 0.5β‡
			bias	var	rmse	bias	var	rmse	bias	var	rmse	bias	var	rmse
0.1	0.25	Known σ	−0.05	1.05	—	−0.10	1.51	—	−0.06	1.05	—	−0.10	1.52	—
		Unspecified σ	−0.09	2.11	0.50	−0.20	2.99	0.50	−0.09	2.11	0.50	−0.21	2.99	0.50
		Constant σ	−0.04	2.03	0.52	−0.18	2.88	0.52	−0.05	2.03	0.52	−0.19	2.88	0.52
		logit-MLE	−0.04	2.71	0.39	−0.44	3.09	0.46	−0.12	2.38	0.44	−0.54	3.01	0.46
		logit-MLE(f)	−0.02	2.59	0.41	−0.35	3.19	0.46	−0.11	2.41	0.44	−0.43	3.11	0.46
	0.50	Known σ	0.00	1.03	—	0.00	1.48	—	−0.01	1.03	—	0.00	1.48	—
		Unspecified σ	−0.01	2.25	0.46	−0.01	3.33	0.45	−0.01	2.25	0.46	−0.01	3.33	0.45
		Constant σ	0.04	2.14	0.48	0.00	3.15	0.47	0.03	2.14	0.48	−0.01	3.15	0.47
		logit-MLE	−0.11	3.60	0.29	−0.20	4.88	0.30	−0.09	3.13	0.33	−0.43	4.27	0.33
		logit-MLE(f)	−0.09	3.39	0.30	−0.21	4.58	0.32	−0.09	3.09	0.33	−0.40	4.17	0.34
	0.75	Known σ	0.10	1.04	—	0.12	1.49	—	0.04	1.03	—	0.09	1.48	—
		Unspecified σ	0.13	2.12	0.49	0.23	3.01	0.49	0.09	2.12	0.49	0.19	3.01	0.49
		Constant σ	0.18	2.02	0.51	0.24	2.88	0.51	0.13	2.02	0.51	0.20	2.88	0.51
		logit-MLE	−1.35	4.96	0.15	−0.29	4.74	0.31	−0.19	3.11	0.33	−0.04	4.11	0.36
		logit-MLE(f)	−0.98	4.32	0.20	−0.09	4.24	0.35	−0.15	2.96	0.35	−0.11	4.04	0.37
0.2	0.25	Known σ	−0.03	0.81	—	−0.06	1.16	—	−0.04	0.81	—	−0.07	1.16	—
		Unspecified σ	−0.05	1.23	0.66	−0.11	1.77	0.65	−0.06	1.23	0.66	−0.12	1.78	0.65
		Constant σ	−0.02	1.19	0.68	−0.10	1.72	0.67	−0.02	1.19	0.68	−0.11	1.73	0.67
		logit-MLE	−0.04	1.59	0.51	−0.24	2.13	0.53	−0.06	1.53	0.53	−0.27	2.17	0.52
		logit-MLE(f)	−0.04	1.57	0.51	−0.21	2.13	0.54	−0.07	1.58	0.51	−0.24	2.14	0.53
	0.50	Known σ	0.00	0.79	—	0.01	1.13	—	0.00	0.79	—	0.00	1.13	—
		Unspecified σ	0.00	1.22	0.65	0.00	1.77	0.64	0.00	1.22	0.65	0.00	1.77	0.64
		Constant σ	0.03	1.18	0.67	0.01	1.70	0.66	0.02	1.18	0.67	0.00	1.70	0.66
		logit-MLE	0.00	1.84	0.43	−0.15	2.37	0.47	−0.05	1.65	0.48	−0.19	2.32	0.48
		logit-MLE(f)	0.00	1.81	0.44	−0.16	2.32	0.48	−0.05	1.68	0.47	−0.17	2.33	0.48
	0.75	Known σ	0.08	0.80	—	0.09	1.15	—	0.03	0.80	—	0.07	1.14	—
		Unspecified σ	0.10	1.23	0.66	0.14	1.77	0.65	0.05	1.22	0.65	0.11	1.76	0.65
		Constant σ	0.13	1.19	0.67	0.15	1.71	0.67	0.08	1.18	0.67	0.11	1.70	0.67
		logit-MLE	0.11	2.09	0.39	0.19	2.52	0.45	0.00	1.77	0.45	−0.01	2.34	0.49
		logit-MLE(f)	0.09	1.90	0.42	0.06	2.44	0.47	0.00	1.75	0.46	−0.06	2.33	0.49

^† b~ = β~ for logit-MLE;

^‡ b~ = 0.5 β~.