Table 3 Performance of different weighted measures of dependence reported as \(100 \int |\hat {C}({\mathbf {u}})- C({\mathbf {u}})|\mathrm {d}{\mathbf {u}} / \int |\hat {C}_{\boldsymbol {\lambda }}({\mathbf {u}})-C({\mathbf {u}})|\mathrm {d}{\mathbf {u}}\) or by a ratio of the kind \(100\,\text {MSE}(\hat {\rho })/\text {MSE}(\hat {\rho }_{\boldsymbol {\lambda }})\)
ρ=0.1 | ρ=0.5 | ρ=0.9 | |||||||
|---|---|---|---|---|---|---|---|---|---|
n=10 | 20 | 50 | n=10 | 20 | 50 | n=10 | 20 | 50 | |
\(\hat {C}_{\boldsymbol {\lambda }}\) | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
\(\hat {C}_{{\boldsymbol {\mu }}}\) | 93 | 93 | 93 | 94 | 95 | 95 | 99 | 99 | 99 |
\(\hat {\rho }_{\boldsymbol {\lambda }}\) | 93 | 94 | 98 | 78 | 87 | 95 | 35 | 48 | 69 |
\(\hat {\rho }_{{\boldsymbol {\mu }}}\) | 60 | 64 | 67 | 53 | 63 | 72 | 33 | 46 | 68 |
\(\hat {\tau }_{\boldsymbol {\lambda }}\) | 79 | 86 | 95 | 76 | 86 | 95 | 66 | 77 | 91 |
\(\hat {\tau }_{{\boldsymbol {\mu }}}\) | 52 | 59 | 65 | 54 | 64 | 72 | 61 | 73 | 88 |
\(\widetilde {\tau }_{{\boldsymbol {\mu }}}\) | 45 | 56 | 63 | 46 | 59 | 70 | 39 | 50 | 72 |