Table 1 Results of the simulation study
| Normal | Uniform | Chi-square | ||
|---|---|---|---|---|
|
60th percentile ρ = 0.2 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 1.74 (0.11) | 0.54 (0.04) | 2.99 (0.25) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 1.73 (0.11) | 0.54 (0.04) | 3.00 (0.26) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.06 (0.20) | − 0.03 (0.06) | 0.63 (0.40) | |
|
60th percentile ρ = 0.5 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 1.89 (0.14) | 0.59 (0.04) | 2.81 (0.28) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 1.88 (0.14) | 0.59 (0.04) | 2.83 (0.29) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.16 (0.21) | − 0.08 (0.06) | 1.38 (0.43) | |
|
60th percentile ρ = 0.7 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 1.95 (0.15) | 0.62 (0.04) | 2.60 (0.31) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 1.94 (0.15) | 0.61 (0.04) | 2.63 (0.32) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.24 (0.22) | − 0.12 (0.07) | 1.82 (0.48) | |
|
80th percentile ρ = 0.2 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 1.96 (0.14) | 0.57 (0.04) | 4.22 (0.27) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 1.96 (0.14) | 0.57 (0.04) | 4.23 (0.28) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.23 (0.26) | − 0.11 (0.07) | 0.25 (0.55) | |
|
80th percentile ρ = 0.5 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 2.22 (0.15) | 0.67 (0.04) | 4.35 (0.31) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 2.22 (0.16) | 0.67 (0.05) | 4.35 (0.32) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.58 (0.25) | − 0.27 (0.07) | 0.50 (0.54) | |
|
80th percentile ρ = 0.7 | \( {\widehat{\overset{\sim }{\beta}}}_1 \) | 2.35 (0.16) | 0.74 (0.05) | 4.35 (0.35) |
| \( {\widehat{\overset{\sim }{\beta}}}_2 \) | 2.36 (0.18) | 0.74 (0.05) | 4.34 (0.35) | |
| \( {\widehat{\overset{\sim }{\beta}}}_3 \) | −0.81 (0.26) | − 0.40 (0.08) | 0.58 (0.56) |