# 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

1. In a practical situation, the confounding would make it impossible to calculate $$\hat {C}$$, $$\hat {\rho }$$ and $$\hat {\tau }$$ on the whole dataset, but they are used here as unattainable ideal benchmarks. Five samples of size n are simulated from a Clayton distribution with Spearman’s correlation ρ. Each scenario is repeated 10,000 times