Table 3.

Bias and variances for the change-point estimate τ̂_n compared for two change-points problem in 3 setups: D: θ^T = (0.3, 1, 1, 1, 0.2, 0.8), E: θ^T = (0.2, 1, 2, 1, 0.4, 0.6) & F: θ^T = (0.3, 1, −1, 1, 0.2, 0.8) (S.D.: Average of estimated standard deviations over 1000 replications; Emp. S.D. : Sample standard deviation based on 1000 replications).

Sample	τ̂1n			τ̂2n
Size	Bias (S.D., Emp. S.D.)		Theo.	Bias × 10−3 (S.D., Emp. S.D.)		Theo.
(n)	× 10−3		S.D.	× 10−3		S.D.
	Existing	Proposed	× 10−3	Existing	Proposed	× 10−3
Set-up D
50	10.2 (63.2, 63.9)	20.3 (63.3, 64.1)	62.0	−11.1 (55.0, 55.5)	−19.2 (55.1, 55.6)	54.0
100	5.1 (44.2, 44.6)	6.3 (44.3, 44.8)	43.8	−4.8 (38.7, 39.2)	−5.9 (38.8, 39.3)	38.2
500	2.8 (19.7, 19.8)	3.7 (19.8, 19.9)	19.6	−3.0 (17.3, 17.5)	−4.0 (17.3, 17.5)	17.1
1000	0.9 (13.9, 13.9)	1.1 (13.9, 14.0)	13.9	−1.0 (12.2, 12.3)	−1.1 (12.2, 12.3)	12.1
5000	0.1 (6.2, 6.2)	0.2 (6.2, 6.2)	6.2	−0.1 (5.4, 5.5)	−0.1 (5.4, 5.5)	5.4
Set-up E
50	−32.9 (14.1, 17.9)	−41.1 (14.8, 19.0)	11.0	40.0 (22.4, 24.1)	51.2 (22.8, 24.9)	21.0
100	−7.2 (9.6, 10.2)	−9.0 (10.0, 10.5)	7.7	8.1 (15.5, 16.4)	9.7 (15.8, 16.7)	14.8
500	−5.1 (3.7, 3.7)	−6.2 (3.7, 3.8)	3.5	6.0 (6.8, 7.0)	6.8 (6.9, 7.1)	6.6
1000	−1.3 (2.5, 2.5)	−1.4 (2.5, 2.5)	2.4	1.4 (4.8, 4.8)	1.5 (4.8, 5.0)	4.7
5000	−0.1 (1.1, 1.1)	−0.1 (1.1, 1.1)	1.1	0.1 (2.1, 2.1)	0.2 (2.1, 2.2)	2.1
Set-up F
50	10.2 (63.2, 64.0)	19.8 (63.3, 64.7)	62.0	−10.4 (55.0, 0.155)	−19.0 (55.3, 55.8)	54.0
100	4.9 (44.0, 44.6)	6.0 (44.3, 44.8)	43.8	−5.3 (38.7, 39.1)	−6.1 (38.8, 39.3)	38.2
500	3.0 (19.7, 19.8)	4.0 (19.8, 19.9)	19.6	−3.8 (17.2, 17.5)	−4.3 (17.3, 17.4)	17.1
1000	0.9 (13.9, 14.0)	1.2 (13.9, 14.0)	13.9	−0.8 (12.1, 12.2)	−1.0 (12.2, 12.3)	12.1
5000	0.1 (6.2, 6.2)	0.1 (6.2, 6.2)	6.2	−0.1 (5.4, 5.5)	−0.1 (5.4, 5.5)	5.4