Table 2 Estimated CP (%), ML (%), MR (%), ML/(ML+MR) and DP (%) of the two-sided 95% CI when N=500, ρ=0 and λ₂=2 for the LR, Fieller’s and delta methods

p

γ

CP

(ML, MR)

\(\frac {\text {ML}}{\text {ML+MR}}\)

DP

CP

(ML, MR)

\(\frac {\text {ML}}{\text {ML+MR}}\)

DP

CP

(ML, MR)

\(\frac {\text {ML}}{\text {ML+MR}}\)

DP

0.1

0

94.59

(4.59, 0.82)

0.85

1.97

94.78

(4.71, 0.51)

0.90

2.72

100

(0, 0)

—

0

0.5

95.24

(2.12, 1.96)

0.52

1.10

96.20

(2.17, 0.86)

0.72

1.28

94.44

(0, 5.56)

0

0

1

96.07

(1.39, 2.38)

0.37

1.14

97.78

(1.27, 0.73)

0.64

1.23

84.05

(0, 15.95)

0

0

1.5

96.56

(0.99, 2.39)

0.29

0.90

98.37

(0.85, 0.72)

0.54

0.98

81.08

(0, 18.92)

0

0

2

96.49

(0.01, 3.50)

0

0.43

98.37

(0.01, 1.62)

0.01

0.43

79.71

(0, 20.29)

0

0

0.3

0

94.88

(2.80, 2.32)

0.55

0.60

94.93

(2.79, 2.28)

0.55

0.61

98.10

(1.89, 0.01)

0.99

0

0.5

95.01

(2.40, 2.54)

0.49

0.14

95.01

(2.40, 2.53)

0.49

0.15

99.13

(0.20, 0.67)

0.23

0

1

95.15

(2.10, 2.71)

0.44

0.08

95.28

(2.09, 2.60)

0.45

0.09

96.37

(0, 3.63)

0

0

1.5

94.81

(2.03, 3.14)

0.39

0.21

95.03

(2.05, 2.90)

0.41

0.22

92.51

(0, 7.49)

0

0

2

94.88

(1.80, 3.32)

0.35

0.08

95.18

(1.78, 3.04)

0.37

0.08

91.80

(0, 8.20)

0

0