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Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions

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Table 1: Simulations under H 0 . J n m n = n 0.6 m n = n 0.7 m n = n 0.8 m n = n 0.9 m n = n 0.95 m n = n 50 0.144 0.079 0.038 0.046 0.041 0.03 100 0.148 0.067 0.07 0.05 0.04 0.033 200 0.129 0.085 0.068 0.043 0.037 0.044 2 500 0.138 0.089 0.05 0.048 0.035
Table 2: Power of the test for γ= d ε(1). J n m n = n 0.6 m n = n 0.7 m n = n 0.8 m n = n 0.9 m n = n 0.95 m n = n 50 0.961 0.919 0.897 0.864 0.829 0
Table 3: Power of the test γ = d Laplace (0, 1) . J n m n = n 0.6 m n = n 0.7 m n = n 0.8 m n = n 0.9 m n = n 0.95 m n = n 50 0.426 0.33 0.3 0.241 0.223 0.163 100 0.658 0.534 0.468 0.365 0.361 0.3 200 0.855 0.824 0.751 0.665 0.613 0.602 2 500 0.998 0.998 0
Table 4: Power of the test γ = d t (3) . I n m n = n 0.6 m n = n 0.7 m n = n 0.8 m n = n 0.9 m n = n 0.95 m n = n 50 0.566 0.445 0.429 0.352 0.321 0.307 100 0.775 0.704 0.647 0.576 0.503 0.454 200 0.942 0.927 0.882 0.833 0.771 0.697 2 500 1 0.997 0.995 0.9
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