ABSTRACT
LetusconsideranullhypothesisoftheformHo:eE~)o,whereE<)o=uyEf'(M)o(y). Thesolutiontothistestingproblemisverysimilartotheonesuggestedaboveinthe caseofanintersectionofsubhypothescs.OnceagainitisbasedonthefactthatIlo iswrongifandonlyifeachofitscomponentsiswrong.Ifeachhypothesisllo(y): ()EC0o(Y)canbetestedusingtherejectionregionWy(ay)=r-1([ty(ay),oo)), satisfyingPe[Wy(ay)]=ay,veE8o(y),itwouldappearnaturaltoconsiderthe overallrejectionregionW(ay.yEf)=nyErWy(ay)foratestofflo.
