Table 2 Simulation results when \(\pmb{\alpha_{0}=2}\)

n = 100

(2, 0.1)

(0.0672, 0.0113)

(0.0658, 0.0108)

(0.0665, 0.0106)

(0.1762, 0.0479)

(2, 0.2)

(0.0751, 0.0086)

(0.0752, 0.0087)

(0.0797, 0.0095)

(0.5044, 0.1226)

(2, 0.3)

(0.0951, 0.0103)

(0.0986, 0.0106)

(0.1146, 0.0121)

(0.1908, 0.0298)

(2, 0.4)

(0.1464, 0.0124)

(0.1591, 0.0133)

(0.1914, 0.0154)

(0.2929, 0.0321)

(2, 0.5)

(0.1706, 0.0097)

(0.1826, 0.0105)

(0.2329, 0.0132)

(0.3307, 0.0209)

(2, 0.6)

(0.2284, 0.0096)

(0.2546, 0.0110)

(0.3457, 0.0140)

(0.4378, 0.0191)

(2, 0.7)

(0.2862, 0.0066)

(0.3291, 0.0077)

(0.4491, 0.0101)

(0.5638, 0.0132)

(2, 0.8)

(0.5566, 0.0065)

(0.7199, 0.0084)

(1.0957, 0.0119)

(1.1036, 0.0358)

(2, 0.9)

(2.0644, 0.0042)

(2.3995, 0.0051)

(3.4865, 0.0075)

(4.1109, 0.0082)

(2, 0.95)

(10.19088, 0.0049)

(11.6877, 0.0057)

(15.3550, 0.0076)

(20.3388, 0.0098)

n = 300

(2, 0.1)

(0.0200, 0.0032)

(0.0202, 0.0032)

(0.0211, 0.0033)

(1.3292, 0.3556)

(2, 0.2)

(0.0288, 0.0041)

(0.0287, 0.0042)

(0.0300, 0.0044)

(0.1811, 0.0696)

(2, 0.3)

(0.0383, 0.0037)

(0.0403, 0.0037)

(0.0456, 0.0041)

(0.0755, 0.0134)

(2, 0.4)

(0.0379, 0.0029)

(0.0419, 0.0034)

(0.0532, 0.0043)

(0.0711, 0.0033)

(2, 0.5)

(0.0548, 0.0035)

(0.0624, 0.0039)

(0.0796, 0.0048)

(0.1052, 0.0075)

(2, 0.6)

(0.0612, 0.0026)

(0.0779, 0.0033)

(0.1276, 0.0049)

(0.1194, 0.0053)

(2, 0.7)

(0.0824, 0.0023)

(0.0961, 0.0025)

(0.1537, 0.0034)

(0.1613, 0.0045)

(2, 0.8)

(0.1095, 0.0014)

(0.1194, 0.0015)

(0.1929, 0.0022)

(0.2158, 0.0027)

(2, 0.9)

(0.3058, 0.0010)

(0.4142, 0.0013)

(0.8087, 0.0022)

(0.6160, 0.0020)

(2, 0.95)

(1.0248, 0.0007)

(1.1210, 0.0008)

(1.7182, 0.0012)

(2.0500, 0.0015)

n = 1,000

(2, 0.1)

(0.0063, 0.0009)

(0.0063, 0.0009)

(0.0064, 0.0009)

(1.0834, 0.2918)

(2, 0.2)

(0.0081, 0.0010)

(0.0084, 0.0010)

(0.0091, 0.0011)

(0.0408, 0.0338)

(2, 0.3)

(0.0102, 0.0009)

(0.0110, 0.0010)

(0.0132, 0.0011)

(0.0192, 0.0025)

(2, 0.4)

(0.0084, 0.0008)

(0.0091, 0.0008)

(0.0116, 0.0010)

(0.0160, 0.0024)

(2, 0.5)

(0.0164, 0.0010)

(0.0193, 0.0011)

(0.0304, 0.0016)

(0.0310, 0.0021)

(2, 0.6)

(0.0124, 0.0005)

(0.0162, 0.0007)

(0.0332, 0.0013)

(0.0239, 0.0010)

(2, 0.7)

(0.0202, 0.0006)

(0.0245, 0.0007)

(0.0496, 0.0011)

(0.0392, 0.0012)

(2, 0.8)

(0.0328, 0.0004)

(0.0406, 0.0005)

(0.0850, 0.0008)

(0.0650, 0.0009)

(2, 0.9)

(0.0706, 0.0002)

(0.1106, 0.0003)

(0.2335, 0.0006)

(0.1391, 0.0004)

(2, 0.95)

(0.1591, 0.0001)

(0.2423, 0.0002)

(0.5047, 0.0003)

(0.3143, 0.0003)