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A.K. Md absolutely continuous Asymptotic Distribution Theory asymptotic joint distribution asymptotic power function asymptotic properties Asymptotic theory asymptotically equivalent Bechhofer Bozivich Carleton University central chisquare chisquare distribution chisquare variables confine ourselves covariance matrix defined degrees of freedom denote effect of preliminary estimate finite Fisher Information following a preliminary freedom respectively genuinely distribution-free H x2 Hence hypothesis H Jensen Khatri Krishnaiah Laguerre polynomials likelihood ratio tests linear models logL LSPTT Math n n,a n,ot non-centrality parameters non-decreasing nonparametric Note nuisance parameter null hypothesis obtain order statistics p-vector parametric counterparts positive definite pq and pq pq degrees pq^a preliminary test pxn pxq rank order tests rank statistics regularity conditions Similarly study the asymptotic tenable test based test for H test of hypothesis test on regression test-function test-statistic testing H three tests Tr H unspecified Xp,a