TABLE 1

The expectations and variances of test statistics

DTDFLD*FF*R2
teαAve.Var.Ave.Var.Ave.Var.Ave.Var.Ave.Var.Ave.Var.
Constant
−0.0410.901−0.0330.973−0.0300.950−0.0401.167−0.0280.7210.202090.00600
0.50.5−0.1210.873−0.1211.011−0.1070.969−0.1421.200−0.1281.1260.149360.00183
1−0.2010.844−0.2121.042−0.1870.982−0.2451.223−0.2201.1310.144580.00170
3−0.5090.739−0.6241.112−0.5530.995−0.6981.267−0.6231.1200.128160.00133
7−0.9020.595−1.3081.058−1.1500.898−1.4111.186−1.2481.0000.108950.00093
∞ (sim)−1.2940.444−2.1700.842−1.8840.673−2.2760.952−1.9850.7640.090710.00059
∞ (cal)−1.2320.505−2.1240.898−1.8600.728−2.1630.721−1.9140.7720.081060.00127
Star−1.4640.265−2.1760.686−2.0180.544−2.2320.716−2.1460.6070.097470.00033
10.5−0.2050.817−0.2061.032−0.1800.968−0.2421.204−0.2151.1080.142710.00161
1−0.3950.732−0.4341.068−0.3760.959−0.4991.219−0.4401.0800.131580.00132
3−1.0590.460−1.4630.998−1.2570.810−1.6011.074−1.3890.8700.097820.00064
7−1.5220.305−2.5120.719−2.1300.546−2.6490.775−2.2660.5940.077100.00036
∞ (sim)−1.7380.237−3.0990.532−2.6030.390−3.2200.587−2.7290.4380.067890.00025
∞ (cal)−1.6850.261−3.0520.560−2.5970.415−3.0980.470−2.6630.4400.057420.00048
Star−1.9000.083−3.0810.339−2.8580.214−3.0810.347−2.8580.2300.068920.00040
30.5−0.5200.574−0.5971.002−0.4950.843−0.6851.108−0.5810.9260.117950.00087
1−1.1700.300−1.5960.864−1.3080.646−1.7630.881−1.4710.6630.086640.00039
3−2.0650.085−3.7460.314−3.0030.210−3.8900.311−3.1710.2130.047950.00009
7−2.2220.062−4.2610.190−3.3970.124−4.3740.197−3.5480.1330.042050.00006
∞ (sim)−2.2780.054−4.4560.152−3.5420.098−4.4580.162−3.6860.1090.039970.00006
∞ (cal)−2.2460.057−4.4160.155−3.5750.101−4.4580.132−3.6420.1060.031340.00009
Star−2.549.001 >−5.0060.014−3.9710.004−4.3440.073−3.7340.0270.039790.00045
  • The expectations and variances of test statistics in the simulated genealogy, rapid-growth-limit genealogy (α = ∞), and star genealogy are shown. The values in the simulated genealogy and limit (sim) are generated by simulation. The values in the star genealogy and the value limit (cal) are obtained by formulas (19)–(28) in the text. Ave., average; Var, variance.