Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size

Table 1

Integrated absolute difference of the cumulative distributions (×100) of 𝑇₁∼𝒩(0,𝑀⁻¹(𝜉^∗,𝜃)), 𝑇₂∼𝒩(0,𝑀⁻¹(𝜉_𝐴,𝜃)), and 𝑇₃∼𝑈𝑄 versus the approximate cumulative distribution of √𝑛(𝜃_𝑛−𝜃) obtained via Monte Carlo simulations for various 𝑛₁ and various moderate sizes of 𝑛. The values 𝜃=1, 𝑥₁=2, 𝜎=.5, 𝑎=.25, and 𝑏=4 were used.

(a) (𝜃=.5)

𝑛1	𝑛=30			𝑛=50			𝑛=100			𝑛=400
	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3
5	19	24	11	16	17	8	15	16	7	14	15	5
10	11	13	8	9	12	7	9	11	6	7	12	4
15	9	10	8	8	9	6	6	9	5	4	10	3

(b) (𝜃=1)

𝑛1	𝑛=30			𝑛=50			𝑛=100			𝑛=400
	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3
5	30	33	25	30	27	19	34	24	12	39	21	6
10	40	40	32	26	27	22	23	28	16	26	20	8
15	34	34	33	27	28	24	21	23	17	18	20	9

(c) (𝜃=1.5)

𝑛1	𝑛=30			𝑛=50			𝑛=100			𝑛=400
	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3	𝑇1	𝑇2	𝑇3
5	32	33	31	39	25	25	42	21	23	42	17	21
10	34	33	22	27	25	16	32	22	10	35	19	12
15	35	35	32	26	26	21	26	22	13	28	21	7