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

Table 9

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

		Near-exact distributions
		2	6	10
		10						82.52872654147179311367711677
	11	190.34577352567912574418958472	190.34577224119045860164933939	190.34577224119046305269448848
	60	88.61692747841779863573642579	88.61692745278611013951753747	88.61692745278611013324695622
	460	83.25188239392602534312672397	83.25188239386900029725019512	83.25188239386900029725019084
15					160.91477802694323358920183897
	16	364.24055367674081921965459933	364.24055364729180144370579916	364.24055364729180141324533927
	65	176.92888004902098965390468116	176.92888004652298399068321382	176.92888004652298398935665716
	465	162.88896091620593405370503267	162.88896091619839192532218731	162.88896091619839192532218500
25					392.50115579019226559339157016
	26	865.98217181891738253073510565	865.98217181564421769408452503	865.98217181564421769411599634
	75	449.82888066877263241039729095	449.82888066790844106600627651	449.82888066790844106598248210
	475	400.06815103634197188114099440	400.06815103633783183795559146	400.06815103633783183795559133
50					1408.73177341938097671969938629
	51	3008.86102439239945267715486761	3008.86102439143486337077345854	3008.86102439143486337077347761
	100	1744.77616968248446695304159926	1744.77616968166143981696831893	1744.77616968166143981696823169
	500	1459.87886196492823624335068318	1459.87886196491897609569196780	1459.87886196491897609569196779
10					92.01002361413199132182815244
	11	226.65802233268160965656246440	226.65802050594440639840352032	226.65802050594440942100275312
	60	98.81456601487869161798863928	98.81456589548535463063927369	98.81456589548535461913454163
	460	92.81648438468645753157179639	92.81648438439817704231467008	92.81648438439817704231465890
15					173.85385431432844593057930059
	16	417.34840709478673000029559780	417.34840705292241842439350332	417.34840705292241840622917724
	65	191.19761414641994048857514633	191.19761413728546916412651829	191.19761413728546916385955487
	465	175.98737199442095758355328501	175.98737199439157553407869592	175.98737199439157553407869464
25					412.29747839373905678663071280
	26	952.93384227143576783559100319	952.93384226668216247367925905	952.93384226668216247369526304
	75	472.65378089035668898963824328	472.65378088767304149154578277	472.65378088767304149156442088
	475	420.24826946954476567253237555	420.24826946953125669939828606	420.24826946953125669939828612
50					1445.59855177795512096240506173
	51	3181.37814988860070147625187269	3181.37814988714219606939294787	3181.37814988714219606939296092
	100	1791.13488232226638659185402987	1791.13488231997376953941120636	1791.13488231997376953941135956
	500	1498.09772807257343724270969706	1498.09772807254669066052003540	1498.09772807254669066052003541