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

Table 5

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

		Near-exact distributions
		2	6	10
		10						81.381015188899104508431120785
	11	189.114696480423388015515754393	189.114697238826289320495944292	189.114697238826277646711500921
	60	87.443617040369847972033082381	87.443617050273318041561932389	87.443617050273318056851954690
	460	82.100788323800277056582786653	82.100788323820173111875365635	82.100788323820173111875372688
15					159.813546850997802977506766879
	16	363.087896604766629226939377100	363.087896734501151262354131399	363.087896734501151251811277829
	65	175.805353263604236148015901820	175.805353269595285156952328009	175.805353269595285157155780468
	465	161.784540428765594956506807022	161.784540428780828916102538276	161.784540428780828916102538558
25					391.438719112192616721837671209
	26	864.891282269279116189851387185	864.891282284150965012514477481	864.891282284150965012477034037
	75	448.748369857001308907641564890	448.748369859173975960465295344	448.748369859173975960473758210
	475	399.002746812117152321633172649	399.002746812124288653675424722	399.002746812124288653675424753
50					1407.69978493252055471492271999
	51	3007.81592652688874585708833686	3007.81592652788317452613238449	3007.81592652788317452613235100
	100	1743.73166206895650376506106613	1743.73166206957708782548197403	1743.73166206957708782548209645
	500	1458.84419233676150570472235786	1458.84419233676635867029771753	1458.84419233676635867029771754
10					90.801532030838687874709640406
	11	225.421470930453454966690527975	225.421472009727318561373265594	225.421472009727311663857900086
	60	97.582829539160859251491143413	97.582829585977762108505255066	97.582829585977762137425094394
	460	91.604850363213970123907600250	91.604850363315475545131468587	91.604850363315475545131487705
15					172.710824396692046362684067121
	16	416.192057135707772720106372243	416.192057320949648013699720809	416.192057320949648008342780372
	65	190.035075104220296563348087039	190.035075126350713655861714506	190.035075126350713655903270996
	465	174.841471634002327233344093337	174.841471634061877548052071914	174.841471634061877548052072072
25					411.209208332240728524234613091
	26	951.840639147683569759583191462	951.840639169340274602907166879	951.840639169340274602887597489
	75	471.550355225483649333455494949	471.550355232304350604344289953	471.550355232304350604337719505
	475	419.157414390428896468907403837	419.157414390452257215547282031	419.157414390452257215547282016
50					1444.55331478957048828683472593
	51	3180.33179707887525737674116194	3180.33179708038051828516553103	3180.33179708038051828516550812
	100	1790.07969304544686923930101362	1790.07969304718352521730352610	1790.07969304718352521730331125
	500	1497.05022951059504341326946354	1497.05022951060908489974722503	1497.05022951060908489974722503