Two Bootstrap Strategies for a 𝑘-Problem up to Location-Scale with Dependent Samples

Table 2

Percentages of rejection, as estimated from 1000 replicates, of the null hypothesis of the equality of 𝐾=2 distributions up to location/scale under Normal and asymmetric Normal dependence structures when 𝑛=200; 𝐹₁ is the Normal distribution; 𝐹₂ is either the 𝒩, 𝑡₉, 𝑡₆, 𝑡₃, or 𝒟ℰ distribution.

Copula	𝐹2	Bootstrap method I			Bootstrap method II
		𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛	𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛
𝐶^𝑁, 𝜏=−1/2	𝒩	5.3	4.0	5.5	2.9	4.7	5.6
	𝑡9	9.5	8.7	10.9	5.6	10.7	10.6
	𝑡6	17.3	13.8	20.5	12.9	21.1	21.0
	𝑡3	76.1	64.2	78.6	75.0	80.3	82.4
	𝒟ℰ	75.0	51.6	79.0	64.7	58.3	76.0
𝐶^𝑁, 𝜏=1/2	𝒩	4.3	4.0	5.5	0.9	3.8	3.7
	𝑡9	11.2	13.3	13.4	6.0	17.7	13.3
	𝑡6	28.0	27.1	32.3	19.2	37.7	33.1
	𝑡3	85.6	76.7	86.5	84.8	91.2	90.0
	𝒟ℰ	87.4	77.4	86.6	77.0	80.9	86.0
𝐾^𝑁, 𝜏=−1/2	𝒩	3.9	4.2	4.0	2.1	5.1	4.4
	𝑡9	10.0	7.6	10.2	6.3	11.0	9.5
	𝑡6	20.9	16.1	20.0	13.9	22.3	19.7
	𝑡3	74.5	64.0	80.2	76.0	82.1	83.1
	𝒟ℰ	74.0	52.8	77.5	63.4	58.9	75.0
𝐾^𝑁, 𝜏=1/2	𝒩	4.9	4.7	4.6	2.0	5.2	3.7
	𝑡9	9.9	10.9	13.8	5.8	14.5	12.8
	𝑡6	25.1	24.1	29.8	17.1	33.7	30.2
	𝑡3	79.8	72.5	84.5	81.2	88.6	88.6
	𝒟ℰ	84.3	72.2	87.7	75.4	78.2	86.7