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Table 1 – Type I Error Rates when p = 2 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α k N1 N2 N3 N4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 2 5 10 -2LogM .0002 .0063 .0184 .0361 .0003 .0059 .0169 .0348 .0007 .0050 .0137 .0325 M-Box .0005 .0106 .0277 .0508 .0008 .0099 .0257 .0491 .0014 .0085 .0213 .0462 8 16 -2LogM .0009 .0067 .0195 .0412 .0003 .0079 .0209 .0460 .0009 .0076 .0214 .0432 M-Box .0013 .0086 .0238 .0485 .0005 .0101 .0255 .0538 .0012 .0098 .0260 .0508 12 24 -2LogM .0006 .0077 .0217 .0452 .0014 .0085 .0218 .0452 .0008 .0078 .0218 .0447 M-Box .0008 .0089 .0244 .0497 .0017 .0098 .0245 .0497 .0009 .0091 .0245 .0491 3 5 10 15 -2LogM .0012 .0086 .0231 .0473 .0011 .0099 .0245 .0500 .0014 .0097 .0257 .0522 M-Box .0010 .0079 .0216 .0449 .0010 .0091 .0230 .0475 .0012 .0089 .0241 .0496 8 16 24 -2LogM .0016 .0112 .0257 .0488 .0014 .0103 .0272 .0517 .0017 .0103 .0264 .0554 M-Box .0016 .0110 .0253 .0482 .0013 .0101 .0267 .0511 .0016 .0101 .0260 .0547 12 24 36 -2LogM .0009 .0082 .0238 .0479 .0012 .0114 .0291 .0550 .0008 .0113 .0279 .0530 M-Box .0009 .0082 .0237 .0477 .0012 .0113 .0290 .0547 .0008 .0112 .0277 .0527 4 5 10 15 20 -2LogM .0007 .0081 .0194 .0396 .0006 .0064 .0188 .0407 .0006 .0077 .0179 .0404 M-Box .0009 .0103 .0237 .0469 .0008 .0082 .0230 .0482 .0009 .0098 .0219 .0479 8 16 24 32 -2LogM .0009 .0105 .0237 .0472 .0006 .0087 .0233 .0473 .0005 .0085 .0238 .0478 M-Box .0010 .0118 .0263 .0514 .0007 .0098 .0258 .0516 .0006 .0096 .0263 .0521 12 24 36 48 -2LogM .0014 .0081 .0227 .0468 .0008 .0090 .0239 .0478 .0013 .0098 .0243 .0483 M-Box .0015 .0088 .0241 .0493 .0009 .0097 .0254 .0504 .0015 .0106 .0259 .0509 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 66 66 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 Table 2 – Type I Error Rates when p = 3 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α k N1 N2 N3 N4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 2 5 10 -2LogM .0012 .0085 .0227 .0491 .0007 .0080 .0269 .0519 .0012 .0092 .0226 .0449 M-Box .0006 .0052 .0154 .0362 .0003 .0048 .0186 .0384 .0006 .0057 .0153 .0328 8 16 -2LogM .0007 .0095 .0247 .0493 .0008 .0092 .0248 .0484 .0006 .0089 .0260 .0512 M-Box .0006 .0087 .0229 .0464 .0007 .0084 .0230 .0456 .0005 .0081 .0242 .0483 12 24 -2LogM .0012 .0111 .0263 .0500 .0008 .0089 .0234 .0507 .0008 .0091 .0235 .0512 M-Box .0011 .0107 .0257 .0490 .0007 .0086 .0228 .0497 .0008 .0088 .0229 .0502 3 5 10 15 -2LogM .0001 .0016 .0065 .0161 .0001 .0018 .0058 .0153 .0001 .0016 .0069 .0171 M-Box .0003 .0049 .0160 .0345 .0004 .0053 .0145 .0330 .0004 .0047 .0168 .0363 8 16 24 -2LogM .0005 .0051 .0144 .0308 .0005 .0047 .0146 .0334 .0003 .0064 .0173 .0356 M-Box .0010 .0083 .0218 .0438 .0009 .0078 .0220 .0472 .0005 .0102 .0258 .0501 12 24 36 -2LogM .0010 .0072 .0180 .0376 .0008 .0063 .0182 .0400 .0004 .0059 .0177 .0404 M-Box .0014 .0095 .0230 .0462 .0012 .0084 .0231 .0490 .0007 .0079 .0225 .0494 4 5 10 15 20 -2LogM .0007 .0092 .0230 .0447 .0010 .0090 .0254 .0496 .0009 .0091 .0256 .0505 M-Box .0003 .0054 .0149 .0310 .0005 .0053 .0166 .0349 .0004 .0053 .0168 .0355 8 16 24 32 -2LogM .0010 .0090 .0219 .0457 .0008 .0089 .0242 .0486 .0015 .0094 .0256 .0522 M-Box .0009 .0080 .0200 .0423 .0006 .0080 .0221 .0451 .0013 .0084 .0235 .0486 12 24 36 48 -2LogM .0011 .0083 .0252 .0507 .0012 .0116 .0264 .0520 .0004 .0107 .0244 .0484 M-Box .0010 .0080 .0245 .0494 .0012 .0112 .0257 .0508 .0004 .0103 .0236 .0472 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 67 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 67 Table 3 – Type I Error Rates when p = 4 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α k N1 N2 N3 N4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 2 5 10 -2LogM .0000 .0005 .0021 .0066 .0000 .0004 .0020 .0071 .0000 .0005 .0025 .0075 M-Box .0000 .0007 .0030 .0092 .0000 .0006 .0029 .0098 .0000 .0007 .0036 .0104 8 16 -2LogM .0003 .0049 .0135 .0327 .0006 .0061 .0170 .0357 .0005 .0055 .0151 .0332 M-Box .0004 .0065 .0173 .0404 .0009 .0081 .0216 .0439 .0008 .0073 .0193 .0410 12 24 -2LogM .0003 .0069 .0186 .0390 .0007 .0076 .0203 .0445 .0012 .0084 .0205 .0425 M-Box .0003 .0083 .0218 .0447 .0009 .0091 .0237 .0507 .0015 .0101 .0239 .0485 3 5 10 15 -2LogM .0006 .0082 .0242 .0522 .0006 .0075 .0234 .0500 .0005 .0081 .0223 .0476 M-Box .0000 .0005 .0029 .0095 .0000 .0005 .0027 .0088 .0000 .0005 .0025 .0082 8 16 24 -2LogM .0008 .0112 .0250 .0525 .0009 .0103 .0258 .0498 .0006 .0102 .0244 .0501 M-Box .0005 .0083 .0194 .0428 .0006 .0076 .0201 .0405 .0004 .0075 .0189 .0408 12 24 36 -2LogM .0011 .0102 .0232 .0491 .0009 .0106 .0258 .0515 .0008 .0113 .0250 .0520 M-Box .0010 .0093 .0215 .0461 .0008 .0097 .0240 .0483 .0007 .0103 .0231 .0489 4 5 10 15 20 -2LogM .0000 .0001 .0004 .0018 .0000 .0001 .0005 .0017 .0000 .0001 .0004 .0015 M-Box .0000 .0006 .0029 .0092 .0000 .0006 .0032 .0091 .0000 .0005 .0027 .0082 8 16 24 32 -2LogM .0001 .0026 .0086 .0207 .0002 .0028 .0087 .0216 .0002 .0035 .0098 .0221 M-Box .0003 .0062 .0179 .0387 .0006 .0065 .0180 .0402 .0007 .0080 .0199 .0409 12 24 36 48 -2LogM .0004 .0055 .0148 .0305 .0002 .0057 .0158 .0333 .0004 .0055 .0156 .0336 M-Box .0008 .0089 .0224 .0438 .0004 .0092 .0238 .0474 .0008 .0089 .0235 .0479 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 68 68 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 Table 4 – Power of -2LogM and M-Box when p = 2 and k = 2 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 d1 d2 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 1 3 -2LogM .0017 .0430 .0990 .1637 .0033 .0371 .0886 .1570 .0055 .0348 .0797 .1503 M-Box .0018 .0433 .0991 .1637 .0036 .0371 .0888 .1570 .0053 .0348 .0797 .1502 1 5 -2LogM .0072 .1089 .2238 .3412 .0137 .1123 2279 .3421 .0216 .0961 .1866 .3215 M-Box .0075 .1102 .2240 .3410 .0160 .1122 .2281 .3420 .0212 .0957 .1873 .3213 1 10 -2LogM .0409 .3580 .5580 .7008 .0553 .3488 .5507 .6940 .1032 .3181 .4991 .6819 M-Box .0429 .3598 .5582 .7008 .0635 .3484 .5512 .6938 .1008 .3176 .5003 .6816 8 16 1 3 -2LogM .0288 .1155 .2288 .3474 .0116 .1312 .2428 .3705 .0293 .1238 .2373 .3542 M-Box .0293 .1154 .2287 .3473 .0130 .1313 .2428 .3698 .0279 .1244 .2371 .3542 1 5 -2LogM .1406 .3796 .5677 .7142 .0722 .4208 .5902 .7426 .1373 .4032 .5916 .7241 M-Box .1424 .3792 .5677 .7141 .0773 .4210 .5904 .7425 .1325 .4046 .5912 .7242 1 10 -2LogM .5991 .8726 .9525 .9801 .4334 .8804 .9489 .9795 .5949 .8777 .9518 .9789 M-Box .6015 .8723 .9525 .9801 .4485 .8805 .9490 .9795 .5852 .8785 .9517 .9789 12 24 1 3 -2LogM .0824 .3078 .4738 .6045 .1273 .3196 .4707 .6080 .0874 .2968 .4644 .6014 M-Box .0849 .3079 .4742 .6048 .1275 .3197 .4709 .6083 .0833 .2990 .4645 .6013 1 5 -2LogM .4214 .7785 .8909 .9448 .5424 .7863 .8892 .9418 .4626 .7784 .8876 .9401 M-Box .4327 .7787 .8917 .9449 .5428 .7863 .8893 .9420 .4516 .7792 .8878 .9401 1 10 -2LogM .9472 .9956 .9991 .9996 .9752 .9967 .9991 .9998 .9572 .9953 .9987 .9999 M-Box .9498 .9956 .9991 .9996 .9752 .9967 .9991 .9998 .9541 .9953 .9987 .9999 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 69 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 69 Table 5 – Power of -2LogM and M-Box when p = 2 and k = 3 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 N3 d1 d2 d3 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 1 1.5 3 -2LogM .0149 .0670 .1370 .2213 .0114 .0727 .1392 .2287 .0155 .0681 .1434 .2316 M-Box .0140 .0669 .1369 .2213 .0117 .0725 .1394 .2287 .0149 .0677 .1433 .2316 1 1.5 5 -2LogM .1095 .3048 .4523 .5863 .0978 .3147 .4640 .5995 .1169 .3282 .4867 .6212 M-Box .1048 .3045 .4521 .5863 .0986 .3140 .4641 .5994 .1153 .3272 .4865 .6211 1 1.5 10 -2LogM .6095 .8418 .9275 .9631 .6032 .8545 .9272 .9622 .6278 .8543 .9340 .9683 M-Box .6019 .8418 .9275 .9631 .6062 .8539 .9272 .9622 .6221 .8535 .9338 .9683 8 16 24 1 1.5 3 -2LogM .0798 .2338 .3494 .4606 .0706 .2240 .3563 .4708 .0879 .2256 .3528 .4832 M-Box .0811 .2341 .3494 .4609 .0695 .2242 .3553 .4708 .0866 .2257 .3529 .4833 1 1.5 5 -2LogM .5163 .7605 .8505 .9079 .5018 .7539 .8603 .9150 .5331 .7581 .8552 .9198 M-Box .5199 .7607 .8506 .9080 .4962 .7542 .8599.9150 .5297 .7582 .8555 .9199 1 1.5 10 -2LogM .9861 .9985 .9994 .9999 .9835 .9975 .9990 .9998 .9863 .9976 .9989 .9997 M-Box .9864 .9985 .9994 .9999 .9830 .9975 .9990 .9998 .9859 .9976 .9989 .9997 12 24 36 1 1.5 3 -2LogM .1888 .4422 .6044 .7128 .2257 .4951 .6415 .7403 .1810 .4942 .6367 .7340 M-Box .1896 .4432 .6045 .7129 .2265 .4948 .6419 .7402 .1816 .4941 .6366 .7339 1 1.5 5 -2LogM .8543 .9598 .9836 .9923 .8764 .9725 .9901 .9953 .8433 .9722 .9885 .9944 M-Box .8557 .9599 .9836 .9923 .8773 .9725 .9902 .9953 .8439 .9721 .9885 .9944 1 1.5 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .9999 .9999 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .9999 .9999 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 70 70 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 Table 6 – Power of -2LogM and M-Box when p = 2 and k = 4 ρ = 0.0 ρ = 0.05 ρ = 0.9 α α α N1 N2 N3 N4 d1 d2 d3 d4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 20 1 1.5 3 5 -2LogM .1115 .3422 .4850 .6046 .1008 .3061 .4654 .6022 .1040 .3337 .4618 .6018 M-Box .1076 .3430 .4850 .6044 .0986 .3063 .4653 .6022 .1071 .3340 .4610 .6019 1 3 5 10 -2LogM .2630 .5961 .7169 .8208 .2506 .5494 .7113 .8161 .2514 .5799 .7112 .8211 M-Box .2537 .5963 .7166 .8204 .2463 .5494 .7113 .8161 .2590 .5800 .7107 .8211 1 1.5 3 10 -2LogM .7408 .9208 .9587 .9800 .7208 .9108 .9593 .9799 .7231 .9186 .9549 .9795 M-Box .7333 .9212 .9586 .9800 .7155 .9110 .9593 .9799 .7309 .9186 .9548 .9795 8 16 24 32 1 1.5 3 5 -2LogM .4572 .7666 .8516 .9109 .4236 .7120 .8369 .9037 .4002 .7539 .8609 .9166 M-Box .4481 .7662 .8519 .9109 .4365 .7283 .8473 .9104 .4002 .7536 .8607 .9166 1 3 5 10 -2LogM .8034 .9573 .9815 .9912 .7708 .9375 .9753 .9907 .7522 .9492 .9798 .9911 M-Box .7974 .9572 .9816 .9912 .7811 .9430 .9775 .9913 .7522 .9491 .9798 .9911 1 1.5 3 10 -2LogM .9909 .9993 .9998 1.000 .9898 .9991 .9999 1.000 .9873 .9990 .9997 .9999 M-Box .9901 .9993 .9998 1.000 .9908 .9992 1.000 1.000 .9873 .9990 .9997 .9999 12 24 36 48 1 1.5 3 5 -2LogM .8979 .9663 .9865 .9946 .8555 .9683 .9877 .9932 .8862 .9696 .9878 .9946 M-Box .8969 .9665 .9864 .9946 .8565 .9683 .9877 .9932 .8890 .9697 .9878 .9946 1 3 5 10 -2LogM .9941 .9993 .9999 1.000 .9901 .9991 .9997 .9999 .9939 .9996 1.000 1.000 M-Box .9937 .9993 .9999 1.000 .9902 .9991 .9997 .9999 .9944 .9997 1.000 1.000 1 1.5 3 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 71 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 71 Table 7 – Power of -2LogM and M-Box when p = 3 and k = 2 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 d1 d2 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 1 3 -2LogM .0037 .0223 .0582 .1184 .0035 .0270 .0699 .1303 .0049 .0290 .0616 .1126 M-Box .0037 .0224 .0582 .1184 .0032 .0269 .0699 .1301 .0049 .0293 .0615 .1126 1 5 -2LogM .0113 .0621 .1373 .2537 .0065 .0577 .1556 .2600 .0138 .0720 .1465 .2411 M-Box .0114 .0621 .1375 .2537 .0062 .0573 .1557 .2599 .0138 .0720 .1463 .2412 1 10 -2LogM .0582 .2278 .4109 .5992 .0336 .2130 .4407 .5991 .0518 .2306 .4007 .5701 M-Box .0585 .2285 .4111 .5993 .0309 .2122 .4410 .5990 .0523 .2321 .4007 .5705 8 16 1 3 -2LogM .0180 .1178 .2243 .3399 .0182 .1112 .2230 .3346 .0155 .1098 .2190 .3394 M-Box .0179 .1187 .2243 .3398 .0183 .1118 .2229 .3350 .0154 .1101 .2195 .3396 1 5 -2LogM .1113 .4220 .6003 .7425 .1125 .4137 .5990 .7288 .1024 .4172 .6202 .7430 M-Box .1110 .4233 .6002 .7425 .1135 .4151 .5990 .7290 .1003 .4179 .6207 .7430 1 10 -2LogM .6053 .9201 .9730 .9888 .6204 .9129 .9705 .9884 .5676 .9072 .9731 .9899 M-Box .6049 .9206 .9729 .9888 .6231 .9133 .9705 .9884 .5626 .9073 .9731 .9899 12 24 1 3 -2LogM .1174 .3675 .5249 .6435 .1024 .3441 .5028 .6479 .0996 .3403 4995 .6457 M-Box .1156 .3657 .5253 .6433 .0970 .3435 .5027 .6479 .1023 .3401 .4994 .6457 1 5 -2LogM .6137 .8817 .9412 .9700 .5537 .8537 .9300 .9673 .5633 .8659 .9367 .9742 M-Box .6093 .8813 .9412 .9700 .5425 .8535 .9300 .9673 .5703 .8657 .9366 .9742 1 10 -2LogM .9934 .9998 .9998 1.000 .9906 .9995 1.000 1.000 .9910 1.000 1.000 1.000 M-Box .9932 .9998 .9998 1.000 .9898 .9995 1.000 1.000 .9914 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 72 72 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 Table 8 – Power of –2LogM and M-Box when p = 3 and k = 3 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 N3 d1 d2 d3 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 1 1.5 3 -2LogM .0082 .0500 .1159 .1939 .0096 .0584 .1114 .1948 .0087 .0537 .1263 .2045 M-Box .0063 .0513 .1160 .1937 .0088 .0585 .1114 .1942 .0080 .0533 .1266 .2044 1 1.5 5 -2LogM .0771 .2660 .4440 .5767 .0795 .2721 .4139 .5628 .0783 .2634 .4416 .5853 M-Box .0615 .2699 .4454 .5762 .0765 .2727 .4141 .5623 .0750 .2607 .4420 .5848 1 1.5 10 -2LogM .5779 .8519 .9359 .9692 .5771 .8587 .9295 .9708 .5829 .8571 .9438 .9760 M-Box .5300 .8550 .9363 .9692 .5687 .8590 .9298 .9708 .5724 .8556 .9439 .9760 8 16 24 1 1.5 3 -2LogM .0660 .2158 .3445 .4650 .0622 .2071 .3453 .4823 .0506 .2437 .3760 .4948 M-Box .0676 .2154 .3446 .4649 .0591 .2075 .3448 .4823 .0450 .2420 .3761 .4949 1 1.5 5 -2LogM .5624 .8154 .8984 .9415 .5646 .8045 .9014 .9484 .5049 .8336 .9080 .9483 M-Box .5664 .8150 .8985 .9415 .5573 .8054 .9014 .9484 .4862 .8330 .9080 .9483 1 1.5 10 -2LogM .9962 .9999 1.000 1.000 .9962 .9996 .9998 .9999 .9947 .9999 1.000 1.000 M-Box .9964 .9999 1.000 1.000 .9958 .9996 .9998 .9999 .9938 .9999 1.000 1.000 12 24 36 1 1.5 3 -2LogM .2961 .5410 .6758 .7756 .2821 .5291 .6787 .7859 .2129 .5025 .6652 .7839 M-Box .2926 .5399 .6758 .7757 .2846 .5286 .6781 .7859 .2254 .5023 .6647 .7838 1 1.5 5 -2LogM .9569 .9903 .9960 .9982 .9549 .9887 .9965 .9983 .9241 .9870 .9952 .9986 M-Box .9556 .9901 .9961 .9982 .9553 .9887 .9965 .9983 .9294 .9870 .9952 .9986 1 1.5 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 73 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 73 Table 9 – Power of –2LogM and M-Box when p = 3 and k = 4 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 N3 N4 d1 d2 d3 d4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 20 1 1.5 3 5 -2LogM .0762 .2984 .4424 .5659 .0900 .2917 .4553 .5840 .0947 .3040 .4680 .6041 M-Box .0746 .2991 .4430 .5653 .0933 .2929 .4553 .5843 .0937 .3037 .4685 .6039 1 3 5 10 -2LogM .2181 .5618 .7122 .8143 .2595 .5669 .7374 .8337 .2367 .5587 .7285 .8305 M-Box .2139 .5624 .7125 .8143 .2679 .5684 .7377 .8338 .2334 .5582 .7295 .8304 1 1.5 3 10 -2LogM .7450 .9403 .9732 .9877 .7790 .9394 .9779 .9903 .7677 .9380 .9776 .9910 M-Box .7409 .9403 .9732 .9877 .7858 .9398 .9779 .9903 .7654 .9378 .9776 .9910 8 16 24 32 1 1.5 3 5 -2LogM .5623 .8149 .8934 .9412 .5199 .8036 .8955 .9437 .6069 .8192 .9038 .9488 M-Box .5688 .8139 .8935 .9412 .5052 .8040 .8955 .9437 .6081 .8188 .9043 .9488 1 3 5 10 -2LogM .8838 .9749 .9899 .9974 .8781 .9780 .9922 .9973 .9112 .9769 .9929 .9975 M-Box .8872 .9748 .9899 .9974 .8695 .9782 .9922 .9973 .9117 .9769 .9929 .9975 1 1.5 3 10 -2LogM .9989 1.000 1.000 1.000 .9988 .9999 .9999 .9999 .9988 .9997 1.000 1.000 M-Box .9989 1.000 1.000 1.000 .9987 .9999 .9999 .9999 .9989 .9997 1.000 1.000 12 24 36 48 1 1.5 3 5 -2LogM .9426 .9885 .9965 .9983 .9493 .9921 .9968 .9985 .9048 .9917 .9963 .9987 M-Box .9413 .9885 .9965 .9983 .9508 .9921 .9968 .9985 .9073 .9916 .9963 .9987 1 3 5 10 -2LogM .9990 .9999 1.000 1.000 .9992 .9999 1.000 1.000 .9974 1.000 1.000 1.000 M-Box .9990 .9999 1.000 1.000 .9992 .9999 1.000 1.000 .9975 1.000 1.000 1.000 1 1.5 3 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-79, 2005 74 74 Rev. Mat. Estat., São Paulo, v.23,n.2, p.59-77, 2005 Table 10 – Power of -2LogM and M-Box when p = 4 and k = 2 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 d1 d2 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 1 3 -2LogM .0000 .0178 .0414 .0844 .0000 .0183 .0426 .0879 .0000 .0193 .0487 .0874 M-Box .0000 .0168 .0412 .0846 .0000 .0183 .0426 .0878 .0000 .0183 .0488 .0875 1 5 -2LogM .0000 .0340 .0737 .1373 .0000 .0324 .0725 .1439 .0000 .0385 .0873 .1566 M-Box .0000 .0329 .0735 .1376 .0000 .0324 .0730 .1438 .0000 .0378 .0878 .1570 1 10 -2LogM .0000 .0959 .1918 .3242 .0000 .0849 .1888 .3340 .0000 .0976 .2149 .3483 M-Box .0000 .0921 .1910 .3247 .0000 .0847 .1894 .3336 .0000 .0945 .2152 .3489 8 16 1 3 -2LogM .0133 .0937 .1848 .3087 .0201 .1055 .2004 .3178 .0167 .1030 .1923 .3020 M-Box .0125 .0932 .1843 .3087 .0205 .1055 .2004 .3178 .0182 .1027 .1924 .3020 1 5 -2LogM .0977 .3800 .5460 .7098 .1370 .4116 .5927 .7292 .1255 .3971 .5687 .7097 M-Box .0910 .3788 .5452 .7098 .1395 .4117 .5927 .7291 .1314 .3963 .5687 .7099 1 10 -2LogM .6019 9165 .9677 .9889 .6911 .9321 .9756 .9899 .6652 .9197 .9710 .9891 M-Box .5852 .9156 .9677 .9890 .6952 .9321 .9755 .9899 .6764 .9192 .9710 .9891 12 24 1 3 -2LogM .0766 .3477 .5108 .6474 .1184 .3686 .5324 .6734 .1601 .3803 .5327 .6610 M-Box .0635 .3471 .5109 .6476 .1183 .3678 .5319 .6733 .1594 .3808 .5322 .6608 1 5 -2LogM .5426 .8950 .9554 .9790 .6534 .9010 .9604 .9850 .7131 .9037 .9573 .9815 M-Box .5042 .8946 .9555 .9790 .6532 .9009 .9604 .9850 .7112 .9040 .9571 .9815 1 10 -2LogM .9931 .9998 1.000 1.000 .9973 .9999 1.000 1.000 .9984 1.000 1.000 1.000 M-Box .9910 .9998 1.000 1.000 .9973 .9999 1.000 1.000 .9984 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 75 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 75 Table 11 – Power of -2LogM and M-Box when p = 4 and k = 3 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 N3 d1 d2 d3 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 1 1.5 3 -2LogM .0030 .0331 .0809 .1465 .0041 .0295 .0769 .1433 .0034 .0304 .0725 .1354 M-Box .0000 .0319 .0812 .1466 .0000 .0313 .0768 .1426 .0000 .0298 .0722 .1354 1 1.5 5 -2LogM .0217 .1340 .2659 .4120 .0234 .1258 .2628 .4059 .0189 .1313 .2552 .3936 M-Box .0000 .1286 .2668 .4128 .0000 .1285 .2616 .4051 .0000 .1282 .2539 .3936 1 1.5 10 -2LogM .2519 .6644 .8378 .9212 .2564 .6478 .8271 .9216 .2411 .6680 .8307 .9132 M-Box .0000 .6566 .8389 .9212 .0000 .6551 .8266 .9213 .0000 .6629 .8300 .9132 8 16 24 1 1.5 3 -2LogM .0528 .2324 .3442 .4777 .0539 .2179 .3450 .4593 .0416 .2205 .3367 .4675 M-Box .0525 .2324 .3437 .4777 .0557 .2180 .3450 .4593 .0426 .2203 .3360 .4677 1 1.5 5 -2LogM .5421 .8489 .9122 .9554 .5548 .8362 .9168 .9528 .5037 .8445 .9138 .9566 M-Box .5401 .8489 .9121 .9554 .5593 .8363 .9166 .9528 .5099 .8442 .9135 .9568 1 1.5 10 -2LogM .9975 1.000 1.000 1.000 .9982 1.000 1.000 1.000 .9970 1.000 1.000 1.000 M-Box .9975 1.000 1.000 1.000 .9983 1.000 1.000 1.000 .9970 1.000 1.000 1.000 12 24 36 1 1.5 3 -2LogM .2850 .5745 .7004 .8033 .2683 .5825 .7166 .8050 .2623 .5925 .7096 .8118 M-Box .2881 .5745 .7005 .8034 .2703 .5830 .7169 .8048 .2626 .5923 .7086 .8118 1 1.5 5 -2LogM .9733 .9957 .9981 .9995 .9676 .9966 .9990 .9996 .9653 .9974 .9991 .9997 M-Box .9740 .9957 .9981 .9995 .9679 .9966 .9990 .9996 .9653 .9974 .9991 .9997 1 1.5 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 76 76 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 Table 12 – Power of -2LogM and M-Box when p = 4 and k = 4 ρ = 0.0 ρ = 0.5 ρ = 0.9 α α α N1 N2 N3 N4 d1 d2 d3 d4 Test .001 .01 .025 .05 .001 .01 .025 .05 .001 .01 .025 .05 5 10 15 20 1 1.5 3 5 -2LogM .0000 .1968 .2988 .4623 .0000 .2001 .3261 .4509 .0000 .2076 .3164 .4534 M-Box .0000 .1698 .3047 .4606 .0000 .1730 .3240 .4550 .0000 .1690 .3146 .4565 1 3 5 10 -2LogM .0000 .4222 .5636 .7269 .0000 .4186 .5858 .7149 .0000 .4278 .5662 .7041 M-Box .0000 .3753 .5701 .7255 .0000 .3739 .5817 .7183 .0000 .3623 .5636 .7071 1 1.5 3 10 -2LogM .0000 .8854 .9402 .9774 .0000 .8862 .9481 .9750 .0000 .8819 .9393 .9742 M-Box .0000 .8623 .9425 .9772 .0000 .8634 .9472 .9754 .0000 .8460 .9387 .9749 8 16 24 32 1 1.5 3 5 -2LogM .5082 .8274 .9128 .9565 .5774 .8338 .9139 .9558 .5762 .8560 .9192 .9581 M-Box .4989 .8284 .9134 .9565 .5753 .8327 .9139 .9558 .5958 .8560 .9186 .9580 1 3 5 10 -2LogM .8878 .9863 .9955 .9983 .9128 .9847 .9948 .9981 .9169 .9887 .9962 .9988 M-Box .8822 .9863 .9955 .9983 .9121 .9847 .9948 .9981 .9237 .9887 .9962 .9987 1 1.5 3 10 -2LogM .9994 1.000 1.000 1.000 .9997 1.000 1.000 1.000 .9997 1.000 1.000 1.000 M-Box .9993 1.000 1.000 1.000 .9997 1.000 1.000 1.000 .9997 1.000 1.000 1.000 12 24 36 48 1 1.5 3 5 -2LogM .9705 .9964 .9991 .9997 .9542 .9956 .9984 .9992 .9693 .9959 .9983 .9994 M-Box .9712 .9964 .9991 .9997 .9542 .9956 .9984 .9992 .9699 .9959 .9983 .9994 1 3 5 10 -2LogM .9998 .9999 1.000 1.000 .9995 1.000 1.000 1.000 .9998 1.000 1.000 1.000 M-Box .9998 .9999 1.000 1.000 .9995 1.000 1.000 1.000 .9998 1.000 1.000 1.000 1 1.5 3 10 -2LogM 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 M-Box 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 77 Rev. Mat. Estat., São Paulo, v.23, n.2, p.59-77, 2005 77