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

Table 3

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

		Near-exact distributions
		2	6	10
		10						77.93052380523042221626519134
	11	186.05876112572581565724084671	186.05432193047513242686020674	186.05432193047314525997232991
	60	84.04125105999276667186524643	84.04108458609231348943338211	84.04108458609231109537970540
	460	78.65634165506500024084199822	78.65633892721702104079228658	78.65633892721702104079204160
15					154.30151616535021445238246295
	16	357.97669643528506074060759290	357.97507556215083974984357415	357.97507556215080939585842368
	65	170.35237275637365647369739224	170.35226008885071534567845906	170.35226008885071540240672638
	465	156.28032082820735784475589844	156.28031868060615422818671849	156.28031868060615422818672130
25					380.80932798326309965351661308
	26	854.70444721767252577468152620	854.70394734650287271287479556	854.70394734650287269133917757
	75	438.20003415718340026159076324	438.19996662815447062882655526	438.19996662815447063138401124
	475	388.38496822730515375937449496	388.38496656458350909591459832	388.38496656458350909591459983
50					1383.96068056800040468077204943
	51	2984.56855943704772921090729785	2984.56844789958359734870454884	2984.56844789958359734870371056
	100	1720.11786940941582246751263410	1720.11783827238527706678307676	1720.11783827238527706678545071
	500	1435.12611970183181982922209152	1435.12611845907109035050829355	1435.12611845907109035050829357
10					87.16571139978756939605535555
	11	222.35460048933098793717199428	222.34999712883572718401028732	222.34999712881867010107412453
	60	94.01616090177012981866436862	94.01591912908288010423242638	94.01591912908288738648975948
	460	87.97774784195631422822549370	87.97774379040648875818772244	87.97774379040648875818827763
15					166.98739013667388353875528529
	16	411.06647044542264851519342470	411.06480936217954062715053117	411.06480936217950312171917698
	65	184.39761554112671734787489011	184.39747019675240094311740291	184.39747019675240137066064190
	465	169.12943676298651871191909376	169.12943392987951859377231013	169.12943392987951859377239666
25					400.31941006633016981735907054
	26	941.63369479396272075223880115	941.63318710455464318301861791	941.63318710455464316544796384
	75	460.78287302204290413806922579	460.78279435481890211302276154	460.78279435481890211439671412
	475	408.28522573430588726946677528	408.28522375722866010999960584	408.28522375722866010999960757
50					1420.50810052822545308190548728
	51	3157.05746081267985238368475051	3157.05734831670317027719825824	3157.05734831670317027719755606
	100	1766.22802929701017442904996266	1766.22799581952383557719092088	1766.22799581952383557718851667
	500	1473.03793287996522918580780119	1473.03793152230567784068549373	1473.03793152230567784068549371