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

Table 4

Percentages of rejection, as estimated from 1000 replicates, of the null hypothesis of the equality of 𝐾=4 distributions up to location/scale under Normal and asymmetric Normal dependence structures when 𝑛=200; 𝐹₁ is the Normal distribution; 𝐹₂=𝐹₃=𝐹₄ are either the 𝒩, 𝑡₉, 𝑡₆, 𝑡₃, or 𝒟ℰ distribution.

Copula	𝐹2=𝐹3=𝐹4	Bootstrap method I			Bootstrap method II
		𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛	𝑆𝑛	𝑇^𝒢1𝑛	𝑇^𝒢2𝑛
𝐶^𝑁, 𝜏=1/3	𝒩	3.8	3.7	3.6	0.7	5.7	2.8
	𝑡9	6.7	6.4	10.7	1.9	11.7	8.8
	𝑡6	12.2	8.4	20.6	7.4	21.0	20.6
	𝑡3	51.4	31.6	74.9	69.2	81.5	84.7
	𝒟ℰ	65.9	35.5	80.8	50.9	57.3	80.9
𝐶^𝑁, 𝜏=2/3	𝒩	3.5	3.2	3.5	0.0	4.2	2.8
	𝑡9	9.4	10.4	15.1	1.3	20.5	12.8
	𝑡6	27.8	23.4	36.0	6.4	48.7	36.2
	𝑡3	76.0	58.6	91.0	84.9	96.3	96.4
	𝒟ℰ	94.0	81.1	97.3	76.9	93.7	97.3
𝐾^𝑁, 𝜏=1/3	𝒩	3.8	3.4	5.0	0.3	5.2	3.5
	𝑡9	7.4	6.6	12.1	1.3	12.7	12.2
	𝑡6	15.1	11.5	17.8	7.7	26.5	19.7
	𝑡3	55.5	34.8	59.9	73.2	85.1	81.7
	𝒟ℰ	69.6	46.7	74.9	54.0	66.8	75.3
𝐾^𝑁, 𝜏=2/3	𝒩	4.3	4.4	4.7	0.4	5.0	3.7
	𝑡9	9.7	11.3	13.5	2.5	16.4	13.1
	𝑡6	24.6	25.6	26.4	9.2	35.0	25.9
	𝑡3	80.8	74.3	82.6	78.1	91.7	89.1
	𝒟ℰ	83.3	75.2	86.2	63.8	82.2	86.7