. Author manuscript; available in PMC: 2018 Aug 9.

Published in final edited form as: Scand Stat Theory Appl. 2013 May 7;41(1):104–140. doi: 10.1111/sjos.12013

Table 3:

Comparing the width of our confidence intervals. On one hand, we test for each sample size n_i if the TMLE-based confidence intervals obtained under $(Q_{0}, g_{n}^{★})$ -adaptive sampling are narrower stochastically than the TMLE-based confidence intervals obtained under i.i.d (Q₀, g^b)-balanced sampling in terms of the two-sample Kolmogorov-Smirnov test. On the other hand, we test for each sample size n_i if the TMLE-based confidence intervals obtained under $(Q_{0}, g_{n}^{★})$ -adaptive sampling are wider stochastically than the TMLE-based confidence intervals obtained under i.i.d (Q₀,g*(Q₀))-optimal sampling in terms of the two-sample Kolmogorov-Smirnov test. We report the p-values (bottom rows, between parentheses). In addition, we report for each sample size n_i the ratios of average widths as defined in (32).

Comparison	Sample size
	n₁	n₂	n₃	n₄	n₅	n₆	n₇
$(Q_{0}, g_{n_{7}}^{★}) v s (Q_{0}, g^{b})$	0.856 (0)	0.871 (0)	0.879 (0)	0.880 (0)	0.878 (0)	0.877 (0)	0.876 (0)
$(Q_{0}, g_{n_{7}}^{★}) v s (Q_{0}, g^{★} (Q_{0}))$	0.962 (0.144)	0.977 (0.236)	0.992 (0.100)	0.995 (0.060)	0.997 (0.407)	1.000 (0.236)	1.000 (0.144)