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

Table 7

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 (51), for different values of and samples of size .

		Near-exact distributions
		2	6	10
		10						82.52872654147179311367711677
	11	190.32756331545176062637260063	190.32756312341501096656402680	190.32756312341502158305183289
	60	88.61292917028511318678026436	88.61292916079636593558509765	88.61292916079636591605025196
	460	83.25135114394460784736871943	83.25135114392165525365869519	83.25135114392165525365868449
15					160.91477802694323358920183897
	16	364.22508588466772907687245064	364.22508590299516153552837462	364.22508590299516166009461668
	65	176.92458777551078581129813667	176.92458777274377296466188482	176.92458777274377296219866202
	465	162.88835115579315719900816060	162.88835115578197146107641778	162.88835115578197146107641501
25					392.50115579019226559339157016
	26	865.97128758699096427158883014	865.97128759463038534181481168	865.97128759463038534192831533
	75	449.82482829542519016999435848	449.82482829549700283679630302	449.82482829549700283676131146
	475	400.06750221064414330250460763	400.06750221064079210854726486	400.06750221064079210854726472
50					1408.73177341938097671969938629
	51	3008.85497566956079322838948966	3008.85497567039266902344201858	3008.85497567039266902344199893
	100	1744.77297987136924686391338212	1744.77297987182100521614403517	1744.77297987182100521614409508
	500	1459.87821714249309834106087509	1459.87821714249577662643142818	1459.87821714249577662643142818
10					92.01002361413199132182815244
	11	226.63967070294372053364533245	226.63967043727843805017814101	226.63967043727844439241178794
	60	98.81015393413627584334298342	98.81015389070350242742117425	98.81015389070350239170134559
	460	92.81589286301973694456386019	92.81589286290397669965973982	92.81589286290397669965971186
15					173.85385431432844593057930059
	16	417.33284870330949699905167521	417.33284873028538888270377699	417.33284873028538894546001788
	65	191.19301774559926635976479112	191.19301773577866477925423064	191.19301773577866477873083849
	465	175.98671397271816998582919704	175.98671397267474771413147408	175.98671397267474771413147254
25					412.29747839373905678663071280
	26	952.92291432362881946300916855	952.92291433479892788245985114	952.92291433479892788251876064
	75	472.64955572272794762005618804	472.64955572304282388887164444	472.64955572304282388889904345
	475	420.24758865175907740683966303	420.24758865174822800295256496	420.24758865174822800295256503
50					1445.59855177795512096240506173
	51	3181.37208704154942688955747637	3181.37208704280924834914384041	3181.37208704280924834914382694
	100	1791.13162751307828413931876980	1791.13162751434597504689343387	1791.13162751434597504689332917
	500	1498.09706702524552623910040811	1498.09706702525328984531816943	1498.09706702525328984531816942