Firstly,thispaperreviewsHall'stheoryofbootstrapcriticalpoints(Hall,1988)andtheEdgeworthexpansionforthemetrodirectionσ=μ(Fn)ofdirectionaldata(Wu&Deng,1996),andthenappliesHall'sresultstostudysixbootstrapconfidenceintervalsforcircularmeandirectionμ=μ(F).OurresultsshowthatSTUD-intervalandABC-intervalarebothsecond-ordercorrect.ForyonMisespopudationM(μ,k),wefindthatsixbootstrapconfidenceintervalsaxeseeond-ordercorrectliketheapproximatenormalconfidenceinterval,andSTUD-intervalisthird-ordercorrect.
