Near-Exact Distributions for Likelihood Ratio Statistics Used in the Simultaneous Test of Conditions on Mean Vectors and Patterns of Covariance Matrices

Table 11

Quantiles of orders and for the chi-square approximation and for the near-exact distributions that match , 6, or 10 exact moments, of for the l.r. statistic in (98), for different values of and samples of size .

		Near-exact distributions
		2	6	10
		10						83.675260742720985209859769504
	11	191.40417508216086413376362096	191.40417507456156657285101953	191.40417507456156582171789369
	60	89.75551474727646979869969732	89.75551474640967644843717358	89.75551474640967644824901262
	460	84.39744286268007803380889520	84.39744286267799553786765774	84.39744286267799553786765754
15					162.015627915781020974421513240
	16	365.27598959457250439641270781	365.27598924568078011317902861	365.27598924568078023771489768
	65	178.02159933390715505406007972	178.02159930927581887701221583	178.02159930927581887281868717
	465	163.98875588508246868863047277	163.98875588500965129426910391	163.98875588500965129426909762
25					393.563502697733190559496512362
	26	867.00163199459511920686859768	867.00163196313224586608216176	867.00163196313224586631572990
	75	450.88354614389745101761538811	450.88354613612423832735039952	450.88354613612423832726057126
	475	401.12939936195988958155797530	401.12939936192330144108737902	401.12939936192330144108737858
50					1409.76374981471409967132946025
	51	3009.86996103494312689347231192	3009.86996103484414649104682359	3009.86996103484414649104682436
	100	1745.80181083720649016504206416	1745.80181083711886310915937759	1745.80181083711886310915937366
	500	1460.90974356899046369444463197	1460.90974356898945187656106283	1460.90974356898945187656106283
10					93.216859660238415548016837195
	11	227.72045780686361924157771904	227.72045779716228291792684432	227.72045779716228232600823452
	60	100.00766587721934070773055100	100.00766587324444064978254945	100.00766587324444064947003150
	460	94.02162317660297597321472166	94.02162317659253570112582966	94.02162317659253570112582916
15					174.996346513999368603209796319
	16	418.38682050544091438546913353	418.38682000788295279610953591	418.38682000788295286039688584
	65	192.32704662492917996667148895	192.32704653485001159062688254	192.32704653485001158976312093
	465	177.12815947623512459860873742	177.12815947595193142347546688	177.12815947595193142347546347
25					413.385621639270785606729896736
	26	953.95532266934168704083850077	953.95532262361714954158839471	953.95532262361714954171095313
	75	473.73022881819913551147338725	473.73022879405047104192607988	473.73022879405047104199617631
	475	421.33473289045564827205481429	421.33473289033629484717703330	421.33473289033629484717703352
50					1446.64377167058432609278629314
	51	3182.38825614178288689315436637	3182.38825614163324534715229586	3182.38825614163324534715229638
	100	1792.17081609574757121169227449	1792.17081609550358487097066245	1792.17081609550358487097066936
	500	1499.14133899336021309354248845	1499.14133899335729098476088160	1499.14133899335729098476088160