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

Table 3

Percentages of rejection, as estimated from 1000 replicates, of the null hypothesis of the equality of 𝐾=3 distributions up to location/scale under Normal and asymmetric Normal dependence structures when 𝑛=200; 𝐹₁ is the Normal distribution; 𝐹₂=𝐹₃ are either the 𝒩, 𝑡₉, 𝑡₆, 𝑡₃, or 𝒟ℰ distribution.

Copula	𝐹2=𝐹3	Bootstrap method I			Bootstrap method II
		𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛	𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛
𝐶^𝑁, 𝜏=1/3	𝒩	4.2	4.3	4.6	0.9	5.1	3.0
	𝑡9	9.3	7.6	12.1	4.0	11.9	10.6
	𝑡6	20.0	14.0	23.2	10.5	25.5	22.1
	𝑡3	60.2	43.4	79.7	74.6	82.4	87.3
	𝒟ℰ	75.1	45.3	79.7	58.8	64.3	79.1
𝐶^𝑁, 𝜏=2/3	𝒩	3.5	3.6	4.9	0.7	4.6	3.6
	𝑡9	12.5	15.3	17.7	2.3	23.5	16.0
	𝑡6	30.9	30.8	39.5	13.5	50.5	40.4
	𝑡3	85.5	71.2	94.0	91.0	97.4	98.1
	𝒟ℰ	96.0	88.9	97.1	85.8	95.7	97.6
𝐾^𝑁, 𝜏=1/3	𝒩	4.7	3.8	4.9	0.8	5.8	4.5
	𝑡9	9.1	8.2	10.7	2.9	11.9	11.0
	𝑡6	20.3	17.9	20.5	14.1	29.1	21.9
	𝑡3	64.4	49.7	69.5	74.5	85.5	84.0
	𝒟ℰ	75.9	54.2	79.3	63.7	71.0	80.2
𝐾^𝑁, 𝜏=2/3	𝒩	3.4	5.5	4.0	0.9	5.7	2.5
	𝑡9	11.8	14.6	14.6	3.7	17.2	13.2
	𝑡6	22.6	25.7	28.7	11.9	37.9	29.6
	𝑡3	81.1	73.8	86.6	80.3	91.9	91.8
	𝒟ℰ	84.2	74.7	85.6	69.3	80.5	85.5