TABLE 2
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Power results (without ZIP and ZINB) with the significant threshold |$\alpha =0.05$|⁠.

|$n=500$|PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.4840.4740.124
 |$x_2$|0.0800.0820.080
Setting 1|$x_3$|0.5940.6080.120
 |$x_4$|0.2760.2780.098
 |$x_5$|0.2740.2600.112
Setting 2|$x_2$|0.0660.0680.090
 |$x_3$|0.3300.2860.126
 |$x_4$|0.0660.0680.366
 |$x_5$|0.0680.0820.384
 |$x_2$|⁠, |$x_3$|0.2920.2700.116
 |$x_4$|⁠, |$x_5$|0.0820.0740.110
|$n=500$|PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.4840.4740.124
 |$x_2$|0.0800.0820.080
Setting 1|$x_3$|0.5940.6080.120
 |$x_4$|0.2760.2780.098
 |$x_5$|0.2740.2600.112
Setting 2|$x_2$|0.0660.0680.090
 |$x_3$|0.3300.2860.126
 |$x_4$|0.0660.0680.366
 |$x_5$|0.0680.0820.384
 |$x_2$|⁠, |$x_3$|0.2920.2700.116
 |$x_4$|⁠, |$x_5$|0.0820.0740.110
n = 2000PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.9980.9920.386
 |$x_2$|0.1220.1560.078
Setting 1|$x_3$|1.0000.9980.384
 |$x_4$|0.9160.9100.210
 |$x_5$|0.8540.8240.298
Setting 2|$x_2$|0.1540.1620.084
 |$x_3$|0.9340.9060.180
 |$x_4$|0.2660.2620.430
 |$x_5$|0.1940.1900.426
 |$x_2$|⁠, |$x_3$|0.9140.8860.084
 |$x_4$|⁠, |$x_5$|0.2180.1980.096
n = 2000PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.9980.9920.386
 |$x_2$|0.1220.1560.078
Setting 1|$x_3$|1.0000.9980.384
 |$x_4$|0.9160.9100.210
 |$x_5$|0.8540.8240.298
Setting 2|$x_2$|0.1540.1620.084
 |$x_3$|0.9340.9060.180
 |$x_4$|0.2660.2620.430
 |$x_5$|0.1940.1900.426
 |$x_2$|⁠, |$x_3$|0.9140.8860.084
 |$x_4$|⁠, |$x_5$|0.2180.1980.096
TABLE 2
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Power results (without ZIP and ZINB) with the significant threshold |$\alpha =0.05$|⁠.

|$n=500$|PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.4840.4740.124
 |$x_2$|0.0800.0820.080
Setting 1|$x_3$|0.5940.6080.120
 |$x_4$|0.2760.2780.098
 |$x_5$|0.2740.2600.112
Setting 2|$x_2$|0.0660.0680.090
 |$x_3$|0.3300.2860.126
 |$x_4$|0.0660.0680.366
 |$x_5$|0.0680.0820.384
 |$x_2$|⁠, |$x_3$|0.2920.2700.116
 |$x_4$|⁠, |$x_5$|0.0820.0740.110
|$n=500$|PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.4840.4740.124
 |$x_2$|0.0800.0820.080
Setting 1|$x_3$|0.5940.6080.120
 |$x_4$|0.2760.2780.098
 |$x_5$|0.2740.2600.112
Setting 2|$x_2$|0.0660.0680.090
 |$x_3$|0.3300.2860.126
 |$x_4$|0.0660.0680.366
 |$x_5$|0.0680.0820.384
 |$x_2$|⁠, |$x_3$|0.2920.2700.116
 |$x_4$|⁠, |$x_5$|0.0820.0740.110
n = 2000PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.9980.9920.386
 |$x_2$|0.1220.1560.078
Setting 1|$x_3$|1.0000.9980.384
 |$x_4$|0.9160.9100.210
 |$x_5$|0.8540.8240.298
Setting 2|$x_2$|0.1540.1620.084
 |$x_3$|0.9340.9060.180
 |$x_4$|0.2660.2620.430
 |$x_5$|0.1940.1900.426
 |$x_2$|⁠, |$x_3$|0.9140.8860.084
 |$x_4$|⁠, |$x_5$|0.2180.1980.096
n = 2000PredictorZIQ-SIRZIQRankQuantile Single-index
 |$x_1$|0.9980.9920.386
 |$x_2$|0.1220.1560.078
Setting 1|$x_3$|1.0000.9980.384
 |$x_4$|0.9160.9100.210
 |$x_5$|0.8540.8240.298
Setting 2|$x_2$|0.1540.1620.084
 |$x_3$|0.9340.9060.180
 |$x_4$|0.2660.2620.430
 |$x_5$|0.1940.1900.426
 |$x_2$|⁠, |$x_3$|0.9140.8860.084
 |$x_4$|⁠, |$x_5$|0.2180.1980.096
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